images images listlengths 1 1 | problem stringlengths 88 589 | answer stringclasses 5
values | problem_id stringlengths 8 10 |
|---|---|---|---|
<image>As shown in the diagram, quadrilateral GBCD is an isosceles trapezoid with a perimeter of 40cm. What is the length of CD?
A. 10 cm;B. 11 cm;C. 12 cm;D. 6 cm; E. No correct answer | A | 2steps_201 | |
<image>A piece of wire can be bent to form the parallelogram shown in the diagram. The length of the wire is ( ) cm.
A. 27; B. 19; C. 18; D. 9; E. No correct answer | C | 2steps_202 | |
<image>As shown in the diagram, it is known that the perimeter of parallelogram ABCD is 16 cm. What is the length of AD in cm?
A. 2; B. 3; C. 4; D. 5; E. No correct answer | D | 2steps_203 | |
<image>As shown in the diagram, the perimeter of the parallelogram is ( )m.
A. 11; B. 2200; C. 220; D. 22; E. No correct answer | D | 2steps_204 | |
<image>As shown in the diagram, it is known that the perimeter of parallelogram ABCD is 60 cm. What is the length of BC?
A. 15 cm ; B. 20 cm ; C. 25 cm ; D. 30 cm ; E. No correct answer | B | 2steps_205 | |
<image>As shown in the diagram, draw the largest possible square inside a circle with a radius of 2 cm. The area of the square is ( ) square centimeters.
A. 16;B. 4;C. 8; D. No correct answer | C | 2steps_206 | |
<image>If the area of the shaded part in the diagram is 16 square centimeters, which of the following expressions is correct?
A. (R^2 - r^2) = 32; B. (R^2 - r^2) = 16; C. (R - r) = 16; D. No correct answer | B | 2steps_207 | |
<image>As shown in the diagram, if the area of the shaded part is 20 square centimeters, which of the following expressions is correct?
A. R^2 - r^2 = 20; B. (R^2 - r^2)π = 10; C. (R - r) = 16; D. No correct answer | A | 2steps_208 | |
<image>As shown in the diagram, there is a quarter-circle inside a square. If the area of the square is 4 cm², what is the side length of the square in cm?
A. 1;B. 2;C. 3; D. No correct answer | B | 2steps_209 | |
<image>As shown in the diagram, if the area of a square is 100 square meters, what is the length of each side of the square in meters?
A. 1; B. 10; C. 100; D. No correct answer | B | 2steps_210 | |
<image>As shown in the diagram, if the shaded is 4 cm², what is its side length (in cm)?
A. 1;B. 2;C. 4; D. No correct answer | B | 2steps_211 | |
<image>As shown in the diagram, each small square has an area of 4 cm². What is the side length of each small square?
A. 4 cm ; B. 3 cm ; C. 2 cm ; D. No correct answer | C | 2steps_212 | |
<image>The rectangle ABCD is as shown in the figure below. The coordinates of points B and C are marked on the diagram. Given that the area of the rectangle is 6cm2, the length of CD is ( )cm.
A. 2;B. 3;C. 4;D. 5; E. No correct answer | A | 2steps_213 | |
<image>As shown in the diagram, the length of the rectangle is as indicated. The area of the rectangle is 32 cm². The width of the rectangle is ( ) cm.
A. 4 cm; B. 6 cm; C. 8 cm; D. 10 cm; E. No correct answer | A | 2steps_214 | |
<image>From a rectangular piece of paper, a circle as shown in the diagram below is cut out. The area of the circle is approximately:
A. 4 square centimeters; B. 3 square centimeters; C. 2 square centimeters; D. 1 square centimeter; E. No correct answer | D | 2steps_215 | |
<image>If the area of the annulus shown in the diagram is 628 cm², which of the following expressions is correct? (π is taken as 3.14)
A. 3.14 × (R² - r²) = 628; B. (R² - r²) = 628; C. 3.14 × (R - r) = 314; D. No correct answer | A | 2steps_216 | |
<image>As shown in the diagram, there is a circular dining table with an approximate surface area of 50 square decimeters. What is the approximate diameter of the dining table? (Assume π = 3.14)
A. 4 dm; B. 6 dm; C. 8 dm; D. 10 dm; E. No correct answer | C | 2steps_217 | |
<image>As shown in the diagram, if the four sides of a square table are lifted up, it becomes a round table. After measurement, the area of the round table is π square meters. What is its diameter?
A. 1; B. 2; C. 3; D. 4; E. No correct answer | B | 2steps_218 | |
<image>As shown in the diagram, the area of trapezoid AECD is 20 square centimeters. What is the length of AE (in cm)?
A. 2;B. 6;C. 4; D. No correct answer | C | 2steps_219 | |
<image>As shown in the diagram, what is the area of this sector?
A. 2π; B. 4π; C. 8π; D. No correct answer | B | 2steps_220 | |
<image>As shown in the diagram, the area of the triangle is 0.06m², and the height of the trapezoid is ( ) m.
A. 0.4;B. 0.6;C. 0.5;D. 1.5; E. No correct answer | A | 2steps_221 | |
<image>If the area of the shaded part in the diagram is 48 square centimeters, what is the height of the triangle (in cm)?
A. 22;B. 8;C. 12; D. No correct answer | C | 2steps_222 | |
<image>As shown in the diagram, the area of triangle ABE is 4 cm². What is the length of AE?
A. 4 cm ; B. 2 cm ; C. 1 cm ; D. No correct answer | A | 2steps_223 | |
<image>As shown in the diagram, it is known that the area of triangle BCD is 6 cm². What is the length of BD?
A. 2 cm ; B. 3 cm ; C. 4 cm ; D. 6 cm ; E. No correct answer | C | 2steps_224 | |
<image>As shown in the diagram, the area of the shape is ( ) square decimeters.
A. 4000;B. 40;C. 20;D. 2000; E. No correct answer | C | 2steps_225 | |
<image>As shown in the diagram, if the area of the parallelogram is 32 cm², what is the height (in cm) between the two parallel sides?
A. 12;B. 10;C. 8;D. 6; E. No correct answer | C | 2steps_226 | |
<image>As shown in the diagram, ∠2 equals ( )°.
A. 52;B. 70;C. 72;D. 38; E. No correct answer | B | 2steps_227 | |
<image>As shown in the diagram, a rectangle paper is folded to form a triangle. If ∠2 = 120°, then ∠3 = ( ).
A. 120°;B. 90°;C. 60°;D. 30°; E. No correct answer | C | 2steps_228 | |
<image>As shown in the diagram, triangle ABO is a right triangle. What is the measure of ∠1 in degrees?
A. 35; B. 55; C. 60; D. No correct answer | A | 2steps_229 | |
<image>Ma Xiaohu accidentally broke a triangular piece of glass. The fragments are shown in the following diagram. What is the missing angle of the triangle in degrees?
A. 105;B. 95;C. 120; D. No correct answer | A | 2steps_230 | |
<image>As shown in the diagram, this is a piece of triangular glass that has shattered, leaving behind a fragment. The missing angle is ( )
A. 105°; B. 90°; C. 110°; D. No correct answer | B | 2steps_231 | |
<image>Given that the triangle in the diagram is an isosceles triangle, what is the degree measure of ∠2?
A. 25° ; B. 35° ; C. 10° ; D. No correct answer | A | 2steps_232 | |
<image>Part of a triangle is covered by an envelope as shown in the diagram. The sum of the two angles that are covered is:
A. 95°;B. 85°;C. 115°; D. No correct answer | C | 2steps_233 | |
<image>In the diagram, ∠P equals ( )
A. 50° ; B. 40° ; C. 30° ; D. No correct answer | B | 2steps_234 | |
<image>As shown in the diagram, it is known that in triangle ABC, ∠B = 50°, and the sum of ∠A and ∠C is:
A. 150°; B. 140°; C. 130°; D. No correct answer | C | 2steps_235 | |
<image>A triangle-shaped piece of paper has one corner torn off (as shown in the diagram). The degree of this angle is ( ).
A. 50°;B. 40°;C. 67°; D. No correct answer | C | 2steps_236 | |
<image>As shown in the diagram, in triangle ABC, ∠B = 80°, ∠A + ∠C = ?
A. 150°; B. 100°; C. 130°; D. No correct answer | B | 2steps_237 | |
<image>What is the degree measure of ∠1?
A. 30°; B. 60°; C. 55°; D. 90°; E. No correct answer | C | 2steps_238 | |
<image>As shown in the diagram, there is a regular hexagon. What is the measure of ∠2?
A. 120°;B. 160°;C. 145°;D. 90°; E. No correct answer | A | 2steps_239 | |
<image>As shown in the diagram, there is a regular pentagon. What is the measure of ∠2?
A. 120°;B. 160°;C. 145°;D. 108°; E. No correct answer | D | 2steps_240 | |
<image>As shown in the diagram, the measure of ∠1 in this regular hexagon is ( )
A. 120°; B. 160°; C. 145°; D. 90°; E. No correct answer | A | 2steps_241 | |
<image>As shown in the diagram, the sum of the interior angles of quadrilateral ABCD is ( )?
A. 180°;B. 540°;C. 360°;D. 720°; E. No correct answer | C | 2steps_242 | |
<image>If a polygon is a regular hexagon, then each of its interior angles is ( )°.
A. 30°;B. 60°;C. 90°;D. 120°; E. No correct answer | D | 2steps_243 | |
<image>Each interior angle of a regular octagon is ( )°.
A. 60°;B. 90°;C. 135°;D. 120°; E. No correct answer | C | 2steps_244 | |
<image>The figure shows a rectangle from which a small square has been cut out. What is the perimeter of the combined shape in terms of the side length of the small square?
A. 6; B. 8; C. 12; D. No correct answer | C | 2steps_245 | |
<image>Linlin is measuring the area of a rectangle by arranging small squares as shown in the diagram. Assuming each small square has a side length of 1 centimeter, what are the length and width of the large rectangle in centimeters?
A. 11, 6;B. 11, 8;C. 12, 8; D. No correct answer | A | 2steps_246 | |
<image>In the diagram, the length and width of the large rectangle are respectively ( ) cm.
A. 7, 5;B. 6, 3;C. 5, 2; D. No correct answer | A | 2steps_247 | |
<image>As shown in the diagram, Fangfang arranged the following figure using small squares with a side length of 1 cm within a large square. How many small squares can make up the side length of the large square?
A. 4; B. 5; C. 6; D. 7; E. No correct answer | C | 2steps_248 | |
<image>As shown in the diagram, which box contains three small circles?
A. A ; B. B ; C. C ; D. D ; E. No correct answer | A | 2steps_249 | |
<image>As shown in the diagram, using square blocks to measure the sides of the rectangle below, AC = ( ) m, BC = ( ) m.
A. 200, 400;B. 400, 200;C. 300, 400;D. 400, 300; E. No correct answer | C | 2steps_250 | |
<image>As shown in the diagram, using rectangular blocks to measure the sides of the rectangle below, AB = ( ) m, BC = ( ) m.
A. 200, 400;B. 400, 200;C. 300, 400;D. 400, 300; E. No correct answer | D | 2steps_251 | |
<image>As shown in the diagram, the road is composed of several equilateral triangles. Observing the distances in the diagram, a = ( ) m, b = ( ) m.
A. 3, 5;B. 4, 3;C. 3, 4;D. 3, 3; E. No correct answer | D | 2steps_252 | |
<image>As shown in the diagram, a square sheet of iron has its corners cut off and is folded to form an open-top cubic iron box. What is the edge length of the cube (in cm)?
A. 3;B. 2;C. 1; D. No correct answer | C | 2steps_253 | |
<image>Fold the figure shown below into a three-dimensional shape. The dimensions of the resulting solid are ( ) cm in length, ( ) cm in width, and ( ) cm in height.
A. 2, 4, 2;B. 2, 2, 4;C. 2, 2, 2; D. No correct answer | C | 2steps_254 | |
<image>As shown in the diagram, among the unfolded figures below, which one is the expanded view of a cube?
A. ①; B. ②; C. ③; D. Cannot be determined; E. No correct answer | C | 2steps_255 | |
<image>As shown in the diagram, there are points A and B on the cube below. Which of the following is the correct expand view of the cube?
A. ①;B. ②;C. ③;D. ④; E. No correct answer | A | 2steps_256 | |
<image>As shown in the diagram, a cube uses 12 meters of steel reinforcement for three of its edges (as shown in the diagram). What is the length of each edge of the cube? (in meters)
A. 4; B. 3; C. 2; D. No correct answer | A | 2steps_257 | |
<image>As shown in the diagram, a three-dimensional frame is constructed using a wooden bar with a total length of 12 cm. What is the edge length of the frame?
A. 1 cm ;B. 2 cm ;C. 3 cm ; D. No correct answer | A | 2steps_258 | |
<image>As shown in the diagram, each face of the solid figure is a ( )?
A. Square;B. Rectangle;C. Cannot be determined; D. No correct answer | A | 2steps_259 | |
<image>As shown in the diagram, to construct a cube frame with an edge length of 1cm on the right, you need ( ) cm of wire.
A. 14;B. 15;C. 12; D. No correct answer | C | 2steps_260 | |
<image>As shown in the diagram, there are two wires of the same length, one forming the frame of a cube on the left, and the other forming the frame of a rectangular cuboid on the right. What is the length of the wire used for the cube frame in cm?
A. 60;B. 70;C. 80;D. 50; E. No correct answer | A | 2steps_261 | |
<image>As shown in the diagram, there are two shapes representing the front and right side of a rectangular cuboid. The length, width, and height of this rectangular cuboid are respectively:
A. 4, 3, 3; B. 5, 4, 3; C. 6, 4, 2; D. 6, 3, 2; E. No correct answer | D | 2steps_262 | |
<image>In the diagram below, the front and right side of a rectangular cuboid are shown. What are the length, width, and height of this rectangular cuboid respectively?
A. 10 cm, 5 cm, 4 cm;B. 5 cm, 10 cm, 4 cm;C. 10 cm, 4 cm, 5 cm; D. No correct answer | A | 2steps_263 | |
<image>There are three types of cardboard, labeled ①, ②, and ③ (with sufficient quantities available). To construct a rectangular cuboid (excluding those with equal length, width, and height) using six pieces of cardboard, which combination should be selected?
A. 4 pieces of type ① cardboard and 2 pieces of type ③ card... | A | 2steps_264 | |
<image>The length of the rectangular cuboid shown in the diagram is 12 cm, and its height is 8 cm. The total area of the two shaded faces is 200 square cm. The width of the rectangular cuboid is ( ) cm.
A. 6 cm;B. 18 cm;C. 10 cm;D. 12 cm; E. No correct answer | C | 2steps_265 | |
<image>The cuboid shown in the diagram below has a total of ________ faces. ( )
A. 6;B. 18;C. 10;D. 12; E. No correct answer | D | 2steps_266 | |
<image>As shown in the diagram, here is a rectangular frame constructed with 16 wooden bars each 1 cm in length. The length, width, and height of the rectangle are respectively ( ) cm.
A. 1, 1, 2; B. 2, 1, 3; C. 2, 1, 1; D. No correct answer | C | 2steps_267 | |
<image>As shown in the diagram, the shapes of each face of the solid figure are ( )?
A. Square; B. Rectangle; C. Both rectangles and squares; D. Cannot be determined; E. No correct answer | C | 2steps_268 | |
<image>As shown in the diagram, what object is formed when a right triangle rotates around side AB for one complete turn?
A. Cylinder;B. Cone;C. Triangular pyramid; D. No correct answer | B | 2steps_269 | |
<image>As shown in the diagram, if each of the two perpendicular sides of a right triangle is rotated around its axis for one complete turn, what solid shapes are formed? What are the radius and height of the base of each shape?
A. Cone - 3cm - 4cm, Cone - 4cm - 3cm; B. Cone - 5cm - 3cm, Cone - 3cm - 4cm; C. Cylinder -... | A | 2steps_270 | |
<image>As shown in the diagram, what object is formed by rotating triangle BC around its side for one full turn, and what are the radius and height of the base?
A. Cone - 3cm - 4cm; B. Cone - 4cm - 3cm; C. Cylinder - 3cm - 4cm; D. Cylinder - 4cm - 3cm; E. No correct answer | B | 2steps_271 | |
<image>As shown in the diagram, what object is formed when an isosceles triangle is rotated around its altitude on the base?
A. Cylinder;B. Cone;C. Triangular pyramid; D. No correct answer | B | 2steps_272 | |
<image>As shown in the diagram, after the lateral surface of this cone is unfolded, what are the radius and arc length of the sector, respectively?
A. 4, 2π;B. 2, 4π;C. 4, π; D. No correct answer | A | 2steps_273 | |
<image>As shown in the diagram, if a rectangle is rotated around the lines containing its length and width respectively, the resulting solid shapes are both ( )?
A. Cylinders;B. Cones;C. Cubes; D. No correct answer | A | 2steps_274 | |
<image>As shown in the diagram, quadrilateral ABCD is a square. What solid shape is formed when it is rotated about side AB?
A. Cylinder; B. Cone; C. Cube; D. No correct answer | A | 2steps_275 | |
<image>In the diagram, rotating the rectangle around line L for one complete turn forms what shape?
A. Cylinder; B. Cone; C. Cube; D. No correct answer | A | 2steps_276 | |
<image>As shown in the diagram, a rectangle has sides of 6 cm and 2 cm. If it is rotated around its shorter side, what solid shape is formed? What are the radius of the base and the height of this solid shape?
A. Cone - 6 cm - 2 cm; B. Cone - 2 cm - 6 cm; C. Cylinder - 6 cm - 2 cm; D. Cylinder - 2 cm - 6 cm; E. No corr... | C | 2steps_277 | |
<image>As shown in the diagram, a rectangle has a length of 6cm and a width of 5cm. If it is quickly rotated as shown in the diagram, what can be obtained?
A. A cylinder with a base diameter of 6cm and a height of 5cm; B. A cylinder with a base radius of 6cm and a height of 5cm; C. A cylinder with a base circumference ... | A | 2steps_278 | |
<image>As shown in the diagram, the circumference of the base of a cylindrical drum is 5cm. When the cylindrical drum rolls one complete revolution on the ground, the shape it traces is ( )?
A. Circle;B. Square;C. Rectangle; D. No correct answer | C | 2steps_279 | |
<image>As shown in the diagram, a rectangle rotates around its 5cm side for one complete turn. The resulting solid figure has a height h = ( ) cm and a radius r = ( ) cm, and is a ( ).
A. 3, 5, cone;B. 5, 3, cylinder;C. rectangular cuboid;D. 3, 5, cylinder; E. No correct answer | B | 2steps_280 | |
<image>As shown in the diagram, a cylinder is vertically cut along the diameter of its base, and the cross-section ABCD is a square. The cross-section ABCD is a square with a side length of 4 cm. The height and the diameter of the base of this cylinder are both equal to ( ) cm.
A. 1;B. 2;C. 3;D. 4; E. No correct answer | D | 2steps_281 | |
<image>As shown in the diagram, there is a cylinder, and Xiao Ming randomly selects two heights on the side of the cylinder, AB and CD. What shape is quadrilateral ABCD?
A. Rectangle;B. Triangle;C. Circle ;D. Cannot be determined; E. No correct answer | A | 2steps_282 | |
<image>The following image is an expanded view of a cuboid (unit: dm). What are the lengths of sides a and b of the shaded area, respectively, in dm?
A. 6, 3;B. 5, 3;C. 7, 3; D. No correct answer | C | 2steps_283 | |
<image>The cardboard box used by the store to package milk is a rectangular cuboid, and the diagram shows the unfolded view of this box. The length, width, and height of this box are respectively ( ) (unit: cm).
A. 8, 6, 4;B. 4, 6, 8;C. 8, 4, 6; D. No correct answer | A | 2steps_284 | |
<image>The following image is an expanded view of a cuboid. Based on the lengths of the line segments in the expanded view, the length, width, and height of the cuboid are respectively ( ) cm.
A. 6, 2, 8;B. 8, 6, 2;C. 8, 2, 6; D. No correct answer | B | 2steps_285 | |
<image>The diagram shows the unfolded view of a rectangular box (unit: cm). What are the length, width, and height of the box?
A. 3, 4, 9;B. 9, 3, 4;C. 9, 4, 3; D. No correct answer | C | 2steps_286 | |
<image>The diagram shows the unfolded view of a rectangular box (unit: cm). From observation, its length, width, and height are respectively:
A. 6, 4, 2;B. 6, 2, 4;C. 2, 4, 6; D. No correct answer | A | 2steps_287 | |
<image>As shown in the diagram, this is an expanded view of a cuboid (unit: cm). Based on the lengths of the line segments in the expanded view, the length, width, and height of the cuboid are respectively:
A. 16, 3, 6;B. 6, 3, 16;C. 16, 6, 3; D. No correct answer | C | 2steps_288 | |
<image>As shown in the diagram, a cuboid is cut along its edges to obtain an expanded view. The lengths of sides a and b in the shaded area are respectively ( ) cm.
A. 6, 3;B. 5, 3;C. 7, 3; D. No correct answer | C | 2steps_289 | |
<image>As shown in the diagram, a rectangular cardboard is cut at each of its four corners, removing a square with a side length of 1cm from each. It is then folded to form an open-top rectangular box with a height of 1cm. The length, width, and height of this box are respectively ( ) cm.
A. 6, 2, 1;B. 5, 2, 1;C. 4, 3,... | A | 2steps_290 | |
<image>As shown in the diagram, a rectangular piece of sheet metal has a section cut from each of its four corners and is then folded to form an open-top rectangular box. The length, width, and height of the box are respectively ( ) cm?
A. 10, 7, 1; B. 12, 5, 1; C. 10, 5, 1; D. No correct answer | C | 2steps_291 | |
<image>As shown in the diagram, after folding it into a three-dimensional figure, the face opposite to face A is face ( ).
A. B; B. C; C. D; D. E; E. No correct answer | C | 2steps_292 | |
<image>Using the rectangular sheet of iron and two circular sheets of iron shown in the diagram, what can be formed?
A. Cylinder;B. Cuboid;C. Cube; D. No correct answer | A | 2steps_293 | |
<image>A rectangular sheet of metal (as shown in the diagram) is used to make a cylindrical box that fits perfectly on its base. There are two different types of circular discs, A and B, with diameters of 2dm and 3dm respectively, and there are two of each type. What are the height and the radius of the base of the cyl... | B | 2steps_294 | |
<image>What are the shapes of the base and the lateral surface of the solid figure shown in the diagram?
A. Circle, Rectangle; B. Triangle, Rectangle; C. Circle, Trapezoid; D. No correct answer | A | 2steps_295 | |
<image>If the lateral surface of a cylinder unfolds into a square as shown in the diagram, then the radius of the base of the cylinder is:(π = 3.14)
A. 1; B. 2; C. 3; D. 4; E. No correct answer | A | 2steps_296 | |
<image>As shown in the diagram, the volume of the small cube that has been cut off in the figure below is ( ) (unit: cubic centimeters).
A. 20 cubic centimeters;B. 8 cubic centimeters;C. 40 cubic centimeters; D. No correct answer | B | 2steps_297 | |
<image>As shown in the figure, there is a rectangular container with a square base of 3 cm on each side. If a small cube is placed inside, the volume of water that rises is ( ) cm³?
A. 27;B. 9;C. 36;D. No correct answer | A | 2steps_298 | |
<image>As shown in the figure, there is a rectangular container filled with water. If a small cube is placed inside, the volume of water that rises is ( ) dm³?
A. 27;B. 64;C. 24;D. No correct answer | B | 2steps_299 | |
<image>Fill a rectangular container with water as shown in the diagram. What is the volume of the water?
A. 120 ; B. 1500 ; C. 1200 ; D. No correct answer | C | 2steps_300 |
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