KS3 Maths · Year 7 · Chapter 6: Surface area and volume of prisms · Lesson 3

Volume of prisms

Year 7About 70 minutesCalculator allowed48 marks

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Quick questions to start.

A1
Needed today
A trapezium has parallel sides of $7$ cm and $11$ cm. The distance between them is $4$ cm. Work out its area.
[1 mark]
Answer
A2
Needed today
A right-angled triangle has shorter sides of $9$ cm and $6$ cm. Work out its area.
[1 mark]
Answer
A3
Last lesson
Work out the total surface area of a cuboid $5$ cm by $3$ cm by $2$ cm.
[1 mark]
Answer
A4
From chapter 4
Increase £ $120$ by $15%$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The cross-section of this prism is a trapezium. Work out the volume of the prism.

Not drawn accurately

Hint Area of a trapezium: half the sum of the parallel sides, times the distance between them.

B1
The cross-section of this prism is a trapezium. Work out the volume of the prism.
[2 marks]
Not drawn accurately
Answer

Example 2

The prism has an L-shaped cross-section. Work out its volume.

Not drawn accurately

Hint Split the L into two rectangles, add their areas, then multiply by the length.

B2
The prism has a T-shaped cross-section. Work out its volume.
[3 marks]
Not drawn accurately
Answer

Example 3

The volume of the triangular prism is $360$ cm³. Work out its length, $l$ .

Not drawn accurately

Hint Find the area of the cross-section, then divide the volume by it.

B3
The cross-section of this prism is a trapezium. The volume of the prism is $480$ cm³. Work out the height, $h$ , of the trapezium.
[3 marks]
Not drawn accurately
Answer $h = \dots\dots$ cm

Practice

Year 7

C1
The cross-section of this prism is an isosceles triangle. Work out the volume of the prism.
[2 marks]
Not drawn accurately
Answer
C2
A wooden wedge holds a door open. It is a prism with a right-angled triangle as its cross-section. Work out its volume in m³.
[3 marks]
Not drawn accurately
Answer

C3
A bar of chocolate is a prism. A bar $8$ cm long has a volume of $96$ cm³. A longer bar has the same cross-section and is $19$ cm long. Work out its volume.
[2 marks]
Answer
C4
A cuboid is $6$ cm long and $4$ cm wide. Its volume is $168$ cm³. Work out its height, $h$ .
[2 marks]
Not drawn accurately
Answer $h = \dots\dots$ cm

Exam-style questions

GCSE Foundation

D1
Leo works out the volume of a triangular prism. The triangle is right-angled with shorter sides of $6$ cm and $10$ cm, and the prism is $9$ cm long. Leo writes $6 \times 10 \times 9 = 540$ cm³.
Leo is wrong. Explain his mistake and work out the correct volume.
[3 marks]
Not drawn accurately
Answer $\dots\dots$ cm³

D2
A swimming pool is $25$ m long and $12$ m wide. The diagram shows its side. The pool is $1.2$ m deep at the shallow end and $2.8$ m deep at the deep end. The bottom slopes evenly.
Not drawn accurately
(a)
Work out the area of the side of the pool.
[2 marks]
Answer
(b)
Work out how many litres of water the pool holds when it is full. ( $1$ m³ $= 1000$ litres.)
[2 marks]
Answer
(c)
A pump fills the pool at $2500$ litres a minute. How many hours does it take to fill the empty pool?
[2 marks]
Answer
Total for D2: 6 marks
D3
A water trough is a prism. Its cross-section is a triangle $40$ cm across the top and $30$ cm deep. The trough holds $54$ litres when it is full. Work out the length of the trough. ( $1$ litre $= 1000$ cm³.)
[4 marks]
Not drawn accurately
Answer
D4
A shed is a prism. Its cross-section is a rectangle $3$ m wide and $2$ m high, with a triangle on top that is $1$ m high. The shed is $4$ m long. Work out the volume of the shed.
[4 marks]
Not drawn accurately
Answer
D5
A pencil is a prism. Its cross-section is a hexagon with an area of $85$ mm². The pencil is $160$ mm long. Work out the volume of the pencil in cm³.
[3 marks]
Not drawn accurately
Answer
D6
A block of metal is a cuboid $12$ cm by $9$ cm by $4$ cm. It is melted down and made into a prism. The cross-section of the prism is a right-angled triangle with shorter sides of $6$ cm and $8$ cm. No metal is lost. Work out the length, $l$ , of the new prism.
[3 marks]
Not drawn accurately
Answer $l = \dots\dots$ cm

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A cuboid has a square cross-section. Its length is $3$ times the side of the square. Its volume is $375$ cm³. Work out the side of the square.
[4 marks]
Hint 1 · What to try
Call the side of the square $x$ . Write the length and the volume in terms of $x$ .
Hint 2 · The first line
The volume is $x \times x \times 3 x = 3 x^{3}$ , so $3 x^{3} = 375$ .
Hint 3 · The full method
$x^{3} = 125$ . Try whole numbers: $5 \times 5 \times 5 = 125$ , so $x = 5$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out the volume of a prism from its cross-section and its length.
I can split a compound cross-section into shapes I know.
I can work backwards from a volume to find a length, in any units.

Answers and mark scheme

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