Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 1: Programme Questions
1. Which of the three solids that Katie slices is not a prism?
2. What words does the computer designer stretch into a prism?
3. Complete: Volume of a prism = Area of _____________ x length.
4. What two shapes make up the cross-section of the freight container used in the aircraft hold?
5. What units does Jamie use for the volume of the container?
6. What is the length of the prism in the ‘Tick or Trash’ item?
7. How many 1cm3 cubes of sugar would fit in the 1m3 box?
8. How many litres of water does the largest tank contain?
9. What formula does Katie use to calculate the area of the cross-section of the triangular fish tank?
10. What shape is the cross-section of the other small fish tank?
© Channel Four Television Corporation 2002
page 1 of 6
Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 2: Tick or Trash
Here are some questions and answers (by Students A and B) on the volume of prisms.
Decide which answers to Tick (correct) and which to Trash (incorrect). Give reasons.
Question 1
Diagram NOT
accurately drawn
6 cm
5 cm
20 cm
8 cm
The diagram shows a prism.
The cross-section of the prism is a trapezium.
The lengths of the parallel sides of the trapezium are 8cm and 6cm.
The distance between the parallel sides of the trapezium is 5cm.
The length of the prism is 20cm.
Work out the volume of the prism.
Student A Answer
Student B Answer
For Area of cross-section use
Volume = area of end x length
1
Area Trapezium = 2 (a +b)h
= 1 (6 + 8) x 5
2
=7x5
= 35
= 1 (6 x 8) x 5
2
= 1 x 14 x 5
2
=
70
2
= 35cm3
Volume = Area of cross-section x length
= 35 x 20
= 700cm3
© Channel Four Television Corporation 2002
page 2 of 6
page 2 of 4
Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 2: Tick or Trash
Question 2
Diagram NOT
accurately drawn
8cm2
xcm
xcm
xcm
The diagram shows a prism.
The prism is made from a cube of side xcm.
A hole of uniform cross-sectional area 8cm2 is cut through the cube.
Find, in terms of x, an expression for the volume of the prism.
Student A Answer
Student B Answer
Area of cross-section = x2 – 8
Volume of large cube = x x x x x = x3
Volume of prism
= x (x2 – 8)
Volume of hole = 8 x 8 x 8 = 512
= x3 – 8 x
Volume of prism = x3 – 512
© Channel Four Television Corporation 2002
page 3 of 6
page 2 of 4
Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 3: Exam Practice Questions (Edexcel)
Question 1
National curriculum reference: S4d
Date: June 1998
Paper: 4
Diagram NOT
accurately drawn
Water is stored in a tank in the shape of a cuboid with a square base. The sides of the base are 30cm long.
The depth of the water is 20cm.
(a) Work out the volume of the water, in cm3.
(2 marks)
More water is put in the tank. The depth of the water rises to 21.6cm.
(b) Calculate the percentage increase in the volume of water in the tank.
(3 marks)
[5]
Question 2
National curriculum reference: S4d
Date: June 1998
Paper: 6
Diagram NOT
accurately drawn
A skip is in the shape of a prism with cross-section ABCD.
AD = 2.3m, DC = 1.3m and BC = 1.7m.
The width of the skip is 1.5m.
(a) Calculate the area of the shape ABCD.
(2 marks)
(b) Calculate the volume of the skip.
(2 marks)
The weight of an empty skip is 650kg.
The skip is full to the top with sand.
1m3 of sand weighs 4300kg.
(c) Calculate the total weight of the skip and the sand.
© Channel Four Television Corporation 2002
(3 marks)
[7]
page 4 of 6
page 3 of 4
Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 3: Exam Practice Questions (Edexcel)
Question 3
National curriculum reference: S4d
Date: June 1995
Paper: 1
In this question you must write down the units of your answer.
Diagram NOT
accurately drawn
(a) Work out the area of the base of the solid shape.
(b) i) Work out the volume of the solid shape.
ii) Write this volume in litres.
[7]
Question 4
National curriculum reference: S4d
Date: November 1997
Paper: 3
The diagram shows a triangular prism.
Diagram NOT
accurately drawn
BC = 4cm, CF = 12cm and angle ABC = 900.
The volume of the triangular prism is 84cm3.
Work out the length of the side AB of the prism.
© Channel Four Television Corporation 2002
[3]
page 5 of 6
page 3 of 4
Maths 4 Real 2
Programme 7 Volume of Prisms
Worksheet 3: Exam Practice Questions (Edexcel)
Question 5
National curriculum reference: S4d
Date: November 1997
Paper: 4
The shape below is the cross-section of a prism 10cm long.
Diagram NOT
accurately drawn
Calculate the volume of the prism.
[3]
Question 6
National curriculum reference: S4d
Date: June 1997
Paper: 3
Diagram NOT
accurately drawn
The diagram shows a cylinder.
The height of the cylinder is 26.3cm.
The diameter of the base of the cylinder is 8.6cm.
Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
[3]
Question 7
National curriculum reference: S4d
Date: June 1997
Paper: 3
Diagram NOT
accurately drawn
This container is made from a cylinder and a cube.
The cylinder has a height of 20cm. It has a base radius of 8cm.
The cube has sides of edges 16cm.
(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 8cm 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.
© Channel Four Television Corporation 2002
[7]
Total = 35
page 6 of 6
page 3 of 4