Question 1

An unopened cylindrical can of baked beans has a height of $	ext{11 cm}$ and a radius of $	ext{4 cm}$
Work out the volume of the can in terms of $\pi$

Accepted Answer

$176 \pi 	ext{ cm}^2$

Answer

$95 \pi 	ext{ cm}^2$

Answer

$131 \pi 	ext{ cm}^2$

Answer

$73 \pi 	ext{ cm}^2$

Question 2

An unopened cylindrical can of baked beans has a height of 11cm and a radius of 4cm.
Work out the surface area of the can to 3 significant figures.

Accepted Answer

$377 	ext{ cm}^2$

Answer

$362 	ext{ cm}^2$

Answer

$179 	ext{ cm}^2$

Answer

$305 	ext{ cm}^2$

Question 3

The triangular prisms shown have the same volume.
Work out the height $h$.

Accepted Answer

$3.3 	ext{ cm}$

Answer

$5.1 	ext{ cm}$

Answer

$1.2 	ext{ cm}$

Answer

$4.7 	ext{ cm}$

Question 4

"The volume of a solid wooden cube is $2 \sqrt{2m}^3$. 
A cylindrical hole, of radius $0.25m,$ is drilled through the length of the cube and its centre.
Work out the total surface area of the six external faces of the resulting solid. Give your answer in the form $a+ b \pi$."

Accepted Answer

$(12 –  \frac{  \pi }{ 8 })	ext{ cm}^2$

Answer

$(8 - 6 \pi)	ext{ cm}^2$

Answer

$(6 + 8 \pi)	ext{ cm}^2$

Answer

$(10 + 2 \pi)	ext{ cm}^2$

Question 5

Karen fills two cylindrical jugs of different sizes with water.
The ratio of the volume of the larger jug to the volume of the smaller jug is $2:1.$
The total volume of the two jugs is $2400\pi	ext{ cm}^3.$
The larger jug has a radius of $	ext{12 cm}.$
Work out the height of the larger jug to $3$ sf.

Accepted Answer

$	ext{11.1 cm}$

Answer

$	ext{23.8 cm}$

Answer

$	ext{18.3 cm}$

Answer

$	ext{32.0 cm}$

Question 6

Karen fills two cylindrical jugs of different sizes with water.
The ratio of the volume of the larger jug to the volume of the smaller jug is 2:1.
The total volume of the two jugs is $2400\pi$cm$^3$.
The larger jug has a radius of 12cm.
Work out the radius of the smaller jug to 3 sf if the radius is equal to the height.

Accepted Answer

$	ext{9.28 cm}$

Answer

$	ext{18.5 cm}$

Answer

$	ext{12.9 cm}$

Answer

$	ext{15.1 cm}$

Question 7

The Great Pyramid of Giza has a square base of length $	ext{230 m}$ and a height of $	ext{147 m}.$
 Work out the volume of the pyramid to $2$ significant figures.

Accepted Answer

$	ext{2600 000 m}^3$

Answer

$	ext{8200 000 m}^3$

Answer

$	ext{450 000 m}^3$

Answer

$	ext{980 000 m}^3$

Question 8

A sphere has surface area of $400 \pi	ext{ cm}^2.$ Work out the radius of the sphere.

Accepted Answer

$	ext{10 cm}$

Answer

$10   \sqrt{3} 	ext{ cm}$

Answer

$10  \pi \sqrt{3} 	ext{ cm}$

Answer

$10 \pi	ext{ cm}$

Question 9

A triangular-based pyramid consists of four equilateral triangles of side length $	ext{8 cm}$. Work out the exact surface area of the pyramid. State your units.

Accepted Answer

$64 \sqrt{3}	ext{ cm}^2$

Answer

$28 \sqrt{2}	ext{ cm}^2$

Answer

$36 \sqrt{5}	ext{ cm}^2$

Answer

$52 \sqrt{5}	ext{ cm}^2$

Question 10

A thin hemispherical bowl has a radius of $	ext{25 cm}.$
How much water could be poured into the bowl before it overflows? Give your answer to $3$ significant figures.

Accepted Answer

$	ext{32 700\ cm}^3$

Answer

$	ext{9290\ cm}^3$

Answer

$	ext{15 900\ cm}^3$

Answer

$	ext{51 200\ cm}^3$

Question 11

A solid cone has height $	ext{24 cm}$ and radius $	ext{10 cm}.$
Work out, in terms of $\pi$, the volume of the cone.

Accepted Answer

$800 \pi	ext{ cm}^3$

Answer

$903 \pi	ext{ cm}^3$

Answer

$450 \pi	ext{ cm}^3$

Answer

$639 \pi	ext{ cm}^3$

Question 12

A solid cone has height $	ext{24 cm}$ and radius $	ext{10 cm}.$
Work out, in terms of $\pi$, the surface area of the cone.

Accepted Answer

$360 \pi	ext{ cm}^2$

Answer

$248 \pi	ext{ cm}^2$

Answer

$450 \pi	ext{ cm}^2$

Answer

$145 \pi	ext{ cm}^2$

Question 13

A cork bottle-stopper is in the form of a frustum of a cone.
The dimensions of the stopper are as shown in the diagram.
Work out, in terms of $\pi$, the volume of cork required to make the stopper.

Accepted Answer

$3996\pi	ext{ mm}^3$

Answer

$1296\pi	ext{ mm}^3$

Answer

$10 048 \pi	ext{ mm}^3$

Answer

$7400\pi	ext{ mm}^3$

Question 14

Teresa models an ice cream cone out of plastic.
The bottom cone part is a solid cone with radius 6cm and height $	ext{15 cm}.$
The top ice cream part is a solid hemisphere.
The base of the hemisphere is the same size as the base of the cone.
Work out, in terms of $\pi$, the volume of plastic Teresa uses to make the model.

Accepted Answer

$324\pi	ext{ cm}^3$

Answer

$158 \pi	ext{ cm}^3$

Answer

$620 \pi	ext{ cm}^3$

Answer

$560 \pi	ext{ cm}^3$

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