Prisms
Question 1
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National curriculum reference: SM2i,4d
Date: June 1998
Paper: 6
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A skip is in the shape of a prism with cross-section ABCD.
AD = 2.3 m, DC = 1.3 m and BC = 1.7 m.
The width of the skip is 1.5 m.
(a) Calculate the area of the shape ABCD.
(b) Calculate the volume of the skip.
(2 marks)
(2 marks)
The weight of an empty skip is 650 kg.
The skip is full to the top with sand.
1 m3 of sand weighs 4300 kg.
(c) Calculate the total weight of the skip and the sand.
(3 marks)
simulatedPageBreakQuestion 2
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National curriculum reference: SM2i,4d
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Date: November 1997
Paper: 3
The diagram shows a triangular prism.
BC = 4 cm, CF = 12 cm and angle ABC = 90º.
The volume of the triangular prism is 84 cm3.
Work out the length of the side AB of the prism.
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National curriculum reference: SM2i,4d
Date: November 1997
Paper: 4
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The shape below is the cross section of a prism 10 cm long.
Calculate the volume of the prism.
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National curriculum reference: SM2i,4a,4d
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Date: June 1996
Paper: 4
This container is made from a cylinder and a cube.
The cylinder has a height of 20 cm. It has a base radius of 8 cm.
The cube has sides of edges 16 cm.
(a) Calculate the total volume, in cm3, of the cylinder. Give your answer to the
nearest cm3.
(b) Calculate the total volume, in cm3, of the container. Give your answer to the
nearest cm3.
When the radius of 8 cm was measured, this measurement was rounded to the nearest
centimetre.
(c) i) Write down the minimum length, in cm, it could be.
ii) Write down the maximum length, in cm, it could be.
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National curriculum reference: SM2i,4d
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Date: June 1999
Paper: 6
A tent has a groundsheet as its horizontal base.
The shape of the tent is a triangular prism of length 8 metres, with two identical half
right-circular cones, one at each end.
The vertical cross-section of the prism is an isosceles triangle of height 2.4 metres and base 3.6
metres.
(a) Calculate the area of the groundsheet.
Give your answer, in m2, correct to one decimal place.
(3 marks)
(b) Calculate the total volume of the tent.
Give your answer, in m2, correct to one decimal place.
(4 marks)
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National curriculum reference: SM4d,4a
Date: June 2000
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The diagram shows a prism.
The cross-section of the prism is a trapezium.
The lengths of the parallel sides of the trapezium are 8 cm and 6 cm.
The distance between the parallel sides of the trapezium is 5 cm.
Paper: 6
The length of the prism is 20 cm.
(a) Work out the volume of the prism.
.................. cm3
(3 marks)
The prism is made out of gold.
Gold has a density of 19.3 grams per cm3.
(b) Work out the mass of the prism.
Give your answer in kilograms.
.................. kilograms
(2 marks)
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National curriculum reference: SM4d
Date: November 2001
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The diagram shows a water tank in the shape of a cuboid.
The measurements of the cuboid are 20 cm by 50 cm by 20 cm.
(a) Work out the volume of the water tank.
.................. cm3
(2 marks)
Water is poured into the tank at a rate of 5 litres per minute.
1 litre = 1000 cm3.
(b) Work out the time it takes to fill the water tank completely.
Give your answer in minutes.
.................. minutes
(2 marks)
Paper: 5
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National curriculum reference: NA5g
Date: March 2002
Paper: 10
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A cube has a surface area of 24a2 square centimetres.
Find a formula, in terms of a, for the volume, V cubic centimetres, of the cube.
V = ........................
(2 marks)
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National curriculum reference: SSM2i
Date: November 2002
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The diagram shows a solid paperweight.
The area of the cross-section ABCDE of the solid paperweight is 130 cm2.
The paperweight is a prism of length 20 cm.
(a) Work out the volume of the paperweight.
...............................
(3 marks)
Paperweights are sold in different sizes.
Paper: 5
The diagrams show the cross-sections of the two mathematically similar
paperweights P and Q.
The height of P is 16 cm.
The height of Q is 24 cm.
The edge of the base of P is 10 cm long.
The edge of the base of Q is x cm long.
(b) Calculate the value of x.
x = ........................
(2 marks)