Volume of a Prism
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Either paper 5 marks
The diagram shows a triangular prism.
(a)Write down the number of faces.
(b)Write down the number of edges.
(c)Write down the number of vertices.
(d)Work out the volume of the prism.
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Either paper 3 marks
A storage box is a cuboid measuring \(20\) cm by \(40\) cm by \(30\) cm.
(a)Calculate the volume of the storage box.
Give your answer in cm\(^3\).
(b)\(1\) litre is \(1000\ \text{cm}^3\).
Calculate the capacity of the storage box in litres.
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Either paper 3 marks
A cube-shaped sponge has a total surface area of \(96\ \text{cm}^2\).
Find the volume of the cube-shaped sponge.
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Either paper 3 marks
The front elevation of a cuboid is shown on the centimetre grid below.
The volume of the cuboid is \(126\ \text{cm}^3\).
The side elevation (viewed from the right-hand side) of the cuboid is a rectangle. Work out its dimensions.
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Either paper 2 marks
The diagram shows a solid cylinder with a diameter of \(8\) cm and a height of \(4\) cm.
Find the volume of the cylinder.
Give your answer in terms of \(\pi\).
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Either paper 4 marks
The diagram shows the cross-section of a prism.
The prism is \(17\) cm long.
(a)Work out the area of the cross-section.
(b)Work out the volume of the prism.
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Either paper 4 marks
Here is the cross-section of a prism.
The volume of the prism is \(70\ \text{cm}^3\).
(a)Find the area of the cross-section.
(b)Find the length of the prism.
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Either paper 2 marks
Ben is going to put boxes into a crate. The crate is a cuboid measuring \(1.6\) m by \(1.2\) m by \(0.8\) m. Each box is a cube of side \(40\) cm.
Ben does these calculations.
volume of crate \(= 1.6 \times 1.2 \times 0.8 = 1.536\) m\(^3\)
volume of one box \(= 0.4 \times 0.4 \times 0.4 = 0.064\) m\(^3\)
number of boxes \(= 1.536 \div 0.064 = 24\)
He claims, "I can put \(24\) boxes in the crate."
Evaluate Ben's method and claim.
You must show your working.
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Either paper 5 marks
Yusuf thinks he can save water by having a shower instead of a bath.
Yusuf's shower uses \(6.5\) litres of water per minute and lasts for \(7\) minutes.
Yusuf assumes that the water in his bath is in the shape of this cuboid.
\(1000\ \text{cm}^3 = 1\) litre
(a)Using Yusuf's assumption, work out how many litres of water he saves by having a shower instead of a bath.
(b)Drawing A shows the cuboid of water in Yusuf's bath when he has filled it.
Drawing A is not drawn to scale. What does drawing A tell you about the amount of water Yusuf saves? Compare it with your answer to part (a).
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Either paper 4 marks
A boat has two possible water tanks, tank A and tank B. Each tank is divided into a fresh-water compartment and a waste-water compartment.
Tank A has a total capacity of \(477\) litres. Its waste-water compartment holds \(275\) litres.
The fresh-water compartment of tank B is a prism with a triangular cross-section. The triangle has a base of \(0.9\) m and a perpendicular height of \(0.5\) m, shown by the dashed line, and the prism is \(1\) m long.
\(1\ \text{m}^3 = 1000\) litres
Joel buys the tank with the greater fresh-water capacity.
Which tank does he buy?
You must show your working.
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(a) \(5\)
(b) \(9\)
(c) \(6\)
(d) \(176\ \text{cm³}\) -
(a) \(24000\ \text{cm}^3\)
(b) \(24\ \text{litres}\) - \(64\ \text{cm}^3\)
- A rectangle \(6\) cm by \(3\) cm
- \(64\pi\ \text{cm}^3\)
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(a) \(112\ \text{cm}^2\)
(b) \(1904\ \text{cm}^3\) -
(a) \(10\ \text{cm}^2\)
(b) \(7\ \text{cm}\) - Claim valid: 4 \(\times\) 3 \(\times\) 2 = 24 boxes. The method only worked because the box side divides every edge exactly, so the boxes leave no gaps.
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(a) \(357.7\ \text{litres}\)
(b) The water is deeper than the assumed cuboid (53 cm compared with 42 cm), so the bath holds more water and Yusuf saves more than \(357.7\) litres. - Tank B: fresh-water capacity \(225\) litres, compared with \(202\) litres for tank A
Takes a couple of seconds the first time a sheet is made.