problem stringlengths 0 1.31k | answer stringclasses 340 values | images images listlengths 1 1 |
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A cylinder has a surface area of 54105 \mathrm{mm}^2 and a radius of 79 mm.
What must the height h mm of the cylinder be?
Round your answer to the nearest whole number. | 30 | |
A cylinder has a surface area of 54105 \mathrm{mm}^2.
What must the height h mm of the cylinder be?
Round your answer to the nearest whole number. | 30 | |
The solid in diagram has a surface area of 54105 \mathrm{mm}^2.
What must the height h mm of the solid be?
Round your answer to the nearest whole number. | 30 | |
A cylinder has a surface area of 54105 mm$^2$.
What must the h mm of the cylinder be?
Round your answer to the nearest whole number. | 30 | |
30 | ||
A wedding cake consists of three cylinders stacked on top of each other. The top layer has a radius and height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.
All the sides and top surfaces are to be covered in icing, but not the bottom.
What is the surface area of the cake that needs to be iced?
Give your answer to the nearest cm2. | 33929 \mathrm{cm}^2 | |
A wedding cake consists of three cylinders stacked on top of each other. The top layer has a height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.
All the sides and top surfaces are to be covered in icing, but not the bottom.
What is the surface area of the cake that needs to be iced?
Give your answer to the nearest cm2. | 33929 \mathrm{cm}^2 | |
A wedding cake consists of three solids stacked on top of each other. The top layer has a height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.
All the sides and top surfaces are to be covered in icing, but not the bottom.
What is the surface area of the cake that needs to be iced?
Give your answer to the nearest cm2. | 33929 \mathrm{cm}^2 | |
A wedding cake consists of three cylinders stacked on top of each other. The middle layer has a radius double of the top layer, and the bottom layer has a radius three times as big.
All the sides and top surfaces are to be covered in icing, but not the bottom.
What is the surface area of the cake that needs to be iced?
Give your answer to the nearest cm2. | 33929 \mathrm{cm}^2 | |
33929 \mathrm{cm}^2 | ||
A square pyramid is shown with the following dimensions, splitted by a middle base. Length of middle base is 8, height of upper square pyramid is 2x+3, height of whole square pyramid is 6x+9.
Find an expression for the length L of the base of the pyramid in terms of the variable, x. | 24 units | |
A square pyramid is shown with the following dimensions. Height of the square pyramid is 6x+9.
Find an expression for the length L of the base of the pyramid in terms of the variable, x. | 24 units | |
A solid is shown with the following dimensions. Height of the solid is 6x+9.
Find an expression for the length L of the base of the solid in terms of the variable, x. | 24 units | |
A square pyramid is shown with the following dimensions.
Find an expression for the length L of the base of the pyramid in terms of the variable, x. | 24 units | |
24 units | ||
The volume of a cylinder that fits exactly into a sphere is given by the formula:
V=\frac{1}{4}\pi h\left(4r^2-h^2\right)
where r is the radius of the sphere and h is the height of the cylinder.
What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm? | 3 | |
Calculate the radius of the sphere shown in figure with the volume of the cylinder 13.75\pi cm3. | 3 | |
Calculate the radius of the sphere shown in figure with the volume of the inside solid 13.75\pi cm3. | 3 | |
Calculate the radius of the sphere shown in figure with the volume of the cylinder 13.75\pi cm$^3$. | 3 | |
3 | ||
A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can). Give your answer rounded down to the nearest cm, to ensure it fits inside the can. | 14 | |
The height is 13 cm. Find L. Give your answer rounded down to the nearest cm. | 14 | |
The height is 13 cm. Find L. Give your answer rounded down to the nearest cm. | 14 | |
Find L. Give your answer rounded down to the nearest cm. | 14 | |
14 | ||
Consider the triangular prism below. Lengths of AB, CF are 10, 4, 15. EX and XF have same length.
Find the length of CX correct to two decimal places. | 15.81 | |
Consider the triangular prism below. Lengths of BC is 4. EX and XF have same length.
Find the length of CX correct to two decimal places. | 15.81 | |
Consider the solid below. Lengths of BC is 4.
Find the length of CX correct to two decimal places. | 15.81 | |
Consider the triangular prism below. EX and XF have same length.
Find the length of CX correct to two decimal places. | 15.81 | |
15.81 | ||
All edges of the following cube are 7 cm long.
Find the exact length of AG in simplest surd form. | \sqrt{147} | |
All edges of the following cube have the same length.
Find the exact length of AG in simplest surd form. | \sqrt{147} | |
All edges of the following solid have the same length.
Find the exact length of AG in simplest surd form. | \sqrt{147} | |
All edges of the following cube have the same length.
Find the exact length of AG in simplest surd form. | \sqrt{147} | |
\sqrt{147} | ||
The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.
The edge length VA is 26cm.
Find the length of VW, the perpendicular height of the pyramid correct to two decimal places. | 23.41 | |
The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.
Find the length of VW, the perpendicular height of the pyramid correct to two decimal places. | 23.41 | |
The following is a solid on a square base with side length 16cm. A right solid has its apex aligned directly above the centre of its base.
Find the length of VW, the perpendicular height of the solid correct to two decimal places. | 23.41 | |
The following is a right pyramid on a square base. A right pyramid has its apex aligned directly above the centre of its base.
Use your answer from part (a) to find the length of VW, the perpendicular height of the pyramid correct to two decimal places. | 23.41 | |
23.41 | ||
A rectangular prism has dimensions as labelled on the diagram. The length, width and height are 9, 4, 5.
Find the length of AG. Leave your answer in surd form. | \sqrt{122} | |
A rectangular prism has dimensions as labelled on the diagram. The height is 5.
Find the length of AG. Leave your answer in surd form. | \sqrt{122} | |
A solid has dimensions as labelled on the diagram. The height is 5.
Find the length of AG. Leave your answer in surd form. | \sqrt{122} | |
A rectangular prism has dimensions as labelled on the diagram.
Find the length of AG. Leave your answer in surd form. | \sqrt{122} | |
\sqrt{122} | ||
Consider the following figure. The base is a triangle with two side of the same length 10cm and one side of length 12cm. The height of the prism is 16cm.
Use Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown. | $x=8 \mathrm{~cm}$ | |
Consider the following figure. The height of the prism is 16cm.
Use Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown. | $x=8 \mathrm{~cm}$ | |
Consider the following figure. The height of the solid is 16cm.
Use Pythagoras' Theorem to find the unknown height $x$ in the solid shown. | $x=8 \mathrm{~cm}$ | |
Consider the following figure.
Use Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown. | $x=8 \mathrm{~cm}$ | |
$x=8 \mathrm{~cm}$ | ||
In the cylindrical tube shown above, the height of the tube is 30 and the circumference of the circular base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38 | C | |
In the cylindrical tube shown above, the circumference of the circular base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38 | C | |
In the tube shown above, the circumference of the base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a surface, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38 | C | |
In the cylindrical tube shown above, the circumference of the circular base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38 | C | |
C | ||
The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\sqrt{3} x$. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6 | A | |
The figure above shows a triangular prism with height $\sqrt{3} x$. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6 | A | |
The figure above shows a solid with height $\sqrt{3} x$. If the volume of the solid is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6 | A | |
The figure above shows a triangular prism. If the volume of the prism is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6 | A | |
A | ||
In the figure shown above, the rectangular container has length, width and height of 6, 5, and 4, and the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2 | D | |
In the figure shown above, the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2 | D | |
In the figure shown above, the left container has radius of 3. If all the water in the right container is poured into the left container, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2 | D | |
In the figure shown above, if all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2 | D | |
D | ||
In the figure above, there is a triangle and two line segments in the figure, and the angle formed by the two segments is x. The two angles labeled in the figure are 55° and 75° respectively. What is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130 | C | |
In the figure above, what is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130 | C | |
In the figure above, what is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130 | C | |
In the figure above, what is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130
| C | |
C | ||
The figure above shows six right triangles. They are put together to form an irregular figure. What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72) | A | |
What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72) | A | |
What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72) | A | |
What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72)
| A | |
A | ||
In quadrilateral PQRS above, the length of QR is 3 and the length of SR is 4. Angle P and angle R are right angles. The length of QP and PS are respectively a and b. What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13 | E | |
What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13 | E | |
What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13 | E | |
What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13
| E | |
E | ||
In the figure above, point O lies on line AB. There are four angles in the figure, which are \frac{x}{6}, \frac{x}{4}, \frac{x}{3}, and \frac{x}{2}. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168 | C | |
In the figure above. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168 | C | |
In the figure above. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168 | C | |
In the figure above. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168
| C | |
C | ||
In triangle ABC above, the bisector of angle BAC is perpendicular to BC at point D. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree | D | |
In triangle ABC above, the bisector of angle BAC is AD. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree | D | |
In triangle ABC above. If AB = 6 and BD = 3, what is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree | D | |
In triangle ABC above, the bisector of angle BAC is AD. The length of AB is equal to the length of AC. What is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree | D | |
D | ||
In the figure above, three lines intersect at a point. The graph consists of the intersection of three lines, two of the angles are y°, and one of the angles is 50°. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85 | A | |
In the figure above. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85 | A | |
In the figure above. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85 | A | |
In the figure above. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85
| A | |
A | ||
In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5} | E | |
In the figure above, the circle has radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5} | E | |
In the figure above, the circle has radius r. What is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5} | E | |
Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}
| E | |
E |
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