images listlengths 0 0 | conversations listlengths 2 2 | id stringlengths 1 5 | source_dataset stringclasses 1
value |
|---|---|---|---|
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54°\nB:64°\nC:27°\nD:37°\n\nYou first think through the reasoning process as an i... | 500 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54°\nB:64°\nC:27°\nD:37°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your ... | 501 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54°\nB:64°\nC:27°\nD:37°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your ... | 502 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then angle CDB = ()\nChoices:\nA:54°\nB:64°\nC:27°\nD:37°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed w... | 503 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nThe given figure... | 504 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the r... | 505 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}... | 506 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}\n\nYou first think through the reasoning process as an intern... | 507 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}\n\nYou first think throu... | 508 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find the leng... | 509 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100°\nB:110°\nC:120°\nD:130°\n\nYou first think through the reasoning process as an internal monologu... | 510 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100°\nB:110°\nC:120°\nD:130°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags... | 511 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100°\nB:110°\nC:120°\nD:130°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags... | 512 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then angle AOC = ()\nChoices:\nA:100°\nB:110°\nC:120°\nD:130°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclos... | 513 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find angle AO... | 514 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoic... | 515 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoic... | 516 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that the radius of circle O is 5.0, chord CD = 8.0, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5√{2}\nD:5√{3}\n\nYou first think through the reasoning process as an internal monologue, enc... | 517 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5√{2}\nD:5√{3}\n\nYou first think through the r... | 518 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nSince the sums o... | 519 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32°\nB:24... | 520 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32°\nB:24°\nC:16°\nD:48°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </th... | 521 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32°\nB:24°\nC:16°\nD:48°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </th... | 522 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Given that AB = 2 DE, then the degree of angle ABC is ()\nChoices:\nA:32°\nB:24°\nC:16°\nD:48°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then,... | 523 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To solve for angle ABC, w... | 524 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThis question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of... | 525 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nangle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44°\nB:22°\nC:46°\nD:36°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer en... | 526 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nangle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44°\nB:22°\nC:46°\nD:36°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer en... | 527 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthen the degree of angle C is ()\nChoices:\nA:44°\nB:22°\nC:46°\nD:36°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\box... | 528 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nSince angle C is... | 529 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50°\nB:30°\nC:25°\nD:20°\n\nYou first think through the reasoning process as... | 530 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50°\nB:30°\nC:25°\nD:20°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then,... | 531 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50°\nB:30°\nC:25°\nD:20°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then,... | 532 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the degree of angle ACD is ()\nChoices:\nA:50°\nB:30°\nC:25°\nD:20°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final an... | 533 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo determine the... | 534 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nShaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:... | 535 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthe distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m\n\nYou first think through the reasoning proces... | 536 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthe distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m\n\nYou first think through the reasoning proces... | 537 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nso the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within... | 538 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To determine the width of... | 539 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that angle α = 130.0, then angle β = ()\nChoices:\nA:30°\nB:40°\nC:50°\nD:65°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, prov... | 540 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that angle α = 130.0, then angle β = ()\nChoices:\nA:30°\nB:40°\nC:50°\nD:65°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, prov... | 541 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that angle α = 130.0, then angle β = ()\nChoices:\nA:30°\nB:40°\nC:50°\nD:65°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, prov... | 542 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then angle β = ()\nChoices:\nA:30°\nB:40°\nC:50°\nD:65°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed wit... | 543 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To solve for angle \\( \\... | 544 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A′B′ in the bridge hole is ()\nChoices:\nA:√... | 545 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A′B′ in the bridge hole is ()\nChoices:\nA:√... | 546 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, When the water surface rises 1.0, the water surface width A′B′ in the bridge hole is ()\nChoices:\nA:√{15}米\nB:2√{15}米\nC:2√{17}米\nD:不能计算\n... | 547 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthe arc ACB is exactly a semicircle. the water surface width A′B′ in the bridge hole is ()\nChoices:\nA:√{15}m\nB:2√{15}m\nC:2√{17}m\nD:no solution\n\nYou first think through the reasoning process as an internal monologue, enclosed within... | 548 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn this problem,... | 549 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nIn the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle... | 550 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nangle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63°\nB:45°\nC:27°\nD:18°\n\nYou first thin... | 551 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nangle CAB = 90.0, angle ABC = 72.0, then the degree of angle ECD is ()\nChoices:\nA:63°\nB:45°\nC:27°\nD:18°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide y... | 552 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAD is the angle bisector of angle CAB, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63°\nB:45°\nC:27°\nD:18°\n\nYou first think through the reasoning process as a... | 553 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\n1. Since angle B... | 554 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6\n\nYou first think through the reasoning process as a... | 555 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6\n\nYou first think through the reasoning process as a... | 556 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6\n\nYou first think through the reasoning process as an internal monologue, enclosed... | 557 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AO is the height of the cone, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then... | 558 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To find the length of AO,... | 559 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35°\nB:45°\nC:55°\nD:70°\n\nYou first think through the reasoning process as an in... | 560 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35°\nB:45°\nC:55°\nD:70°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> ... | 561 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35°\nB:45°\nC:55°\nD:70°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your f... | 562 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, arc AB = arc BC = arc CD, then angle BDC = ()\nChoices:\nA:35°\nB:45°\nC:55°\nD:70°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide yo... | 563 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nNotice that arc ... | 564 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()\nChoices:\nA:πcm²\nB:\\frac{2}{3}πcm... | 565 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, and the area of the shaded part in the figure is ()\nChoices:\nA:πcm²\nB:\\frac{2}{3}πcm²\nC:\\frac{1}{2}cm²\nD:\\frac{2}{3}cm²\n\nYou first think... | 566 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the sector OAB with a radius of 1.0, and the area of the shaded part in the figure is ()\nChoices:\nA:πcm²\nB:\\frac{2}{3}πcm²\nC:\\frac{1}{2}cm²\nD:\\frac{2}{3}cm²\n\nYou first think through the reasoning proce... | 567 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and the area of the shaded part in the figure is ()\nChoices:\nA:πcm²\nB:\\frac{2}{3}πcm²\nC:\\frac{1}{2}cm²\nD:\\frac{2}{3}cm²\n\nYou first think through the reasoning process as an internal monologue, enclosed wi... | 568 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "Let's start by considerin... | 569 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()\nChoices:\nA:2πcm\nB:3πcm\nC:4πcm\nD:5πcm\n... | 570 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap, then the bottom perimeter of the paper cap is ()\nChoices:\nA:2πcm\nB:3πcm\nC:4πcm\nD:5πcm\n\nYou first think through ... | 571 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector paper sheet with a central angle of 120.0 and a radius of 6.0, then the bottom perimeter of the paper cap is ()\nChoices:\nA:2πcm\nB:3πcm\nC:4πcm\nD:5πcm\n\nYou first think through the reasoning process as an internal monolog... | 572 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthen the bottom perimeter of the paper cap is ()\nChoices:\nA:2πcm\nB:3πcm\nC:4πcm\nD:5πcm\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer e... | 573 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nThe bottom perim... | 574 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThe picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of paper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60π\nB:65π\nC:78π\... | 575 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThe length of its generatrix l is 13.0 and its height h is 12.0. The area of paper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60π\nB:65π\nC:78π\nD:156π\n\nYou first think through the reasoning process as ... | 576 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThe length of its generatrix l is 13.0 and its height h is 12.0. The area of paper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60π\nB:65π\nC:78π\nD:156π\n\nYou first think through the reasoning process as ... | 577 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThe area of paper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60π\nB:65π\nC:78π\nD:156π\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. The... | 578 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find the area... | 579 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()\nChoices:\nA:3cm\nB:2√{2}cm\nC:3√{2}cm\nD:4√{2}cm\... | 580 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector piece of paper with a central angle of 120.0 and a radius of 3.0, then the height of the paper is ()\nChoices:\nA:3cm\nB:2√{2}cm\nC:3√{2}cm\nD:4√{2}cm\n\nYou first think through the reasoning process as an internal monologue,... | 581 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nUse a sector piece of paper with a central angle of 120.0 and a radius of 3.0, then the height of the paper is ()\nChoices:\nA:3cm\nB:2√{2}cm\nC:3√{2}cm\nD:4√{2}cm\n\nYou first think through the reasoning process as an internal monologue,... | 582 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nthen the height of the paper is ()\nChoices:\nA:3cm\nB:2√{2}cm\nC:3√{2}cm\nD:4√{2}cm\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclose... | 583 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To find the height of the... | 584 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6\n\nYou first think through the reasoning process as an i... | 585 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6\n\nYou first think through the reasoning process as an i... | 586 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6\n\nYou first think through the reasoning process as an i... | 587 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer en... | 588 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nThe radius of th... | 589 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of this sector cardboard is ()\nChoices:\n... | 590 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat. If the radius of the bottom surface of the conical hat is 10.0, then the area of this sector cardboard is ()\nChoices:\nA:240πcm^{2}\nB:480πcm^{... | 591 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat. If the radius of the bottom surface of the conical hat is 10.0, then the area of this sector cardboard is ()\nChoices:\nA:240πcm^{2}\nB:480πcm^{... | 592 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the area of this sector cardboard is ()\nChoices:\nA:240πcm^{2}\nB:480πcm^{2}\nC:1200πcm^{2}\nD:2400πcm^{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> ... | 593 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nThe area of a se... | 594 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of the cone is ()\nChoices:\nA:3πcm^{2}\nB:9πcm^{2}\nC:16πcm^{2}\nD:25πcm^{2}\n\nYou first think thr... | 595 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the bottom area of the cone is ()\nChoices:\nA:3πcm^{2}\nB:9πcm^{2}\nC:16πcm^{2}\nD:25πcm^{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags.... | 596 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the bottom area of the cone is ()\nChoices:\nA:3πcm^{2}\nB:9πcm^{2}\nC:16πcm^{2}\nD:25πcm^{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags.... | 597 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the bottom area of the cone is ()\nChoices:\nA:3πcm^{2}\nB:9πcm^{2}\nC:16πcm^{2}\nD:25πcm^{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags.... | 598 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find the area... | 599 | AI4Math_MathVerse/baseline/rollout_8 |
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