KS3 Maths · Year 8 · Chapter 10: Surface area and volume of cylinders · Lesson 1

Volume of a cylinder

Year 8About 70 minutesCalculator allowed46 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/ks3-year-8-volume-of-a-cylinder/

Date

Do Now

Quick questions to start.

A1
Needed today
Work out the area of a circle of radius $5$ cm, to $1$ d.p.
[1 mark]
Answer
A2
Needed today
A prism has a cross-section of area $12$ cm² and length $7$ cm. Find its volume.
[1 mark]
Answer
A3
Last lesson
Do sides $6$ , $9$ and $11$ make a right-angled triangle?
[1 mark]
Answer
A4
Year 7
Write $3.5$ litres in cm³.
[1 mark]
Answer

Example, then your turn

Year 8

Your teacher works through each example with you. Then try the one beside it. A cylinder is a prism with a circle as its cross-section, so $V = π r^{2} h$ .

Example 1

Work out the volume of this cylinder, to $3$ s.f.

Hint Area of the end

= π r^{2}

. Multiply by the height.

B1
Work out the volume of this cylinder, to $3$ s.f.
[2 marks]
Answer $\dots$ cm³

Example 2

Work out the volume of this cylinder. Give your answer in terms of $π$ .

Hint Keep

π

as a letter: work out

r^{2} h

and write

π

after it.

B2
Work out the volume of this cylinder. Give your answer in terms of $π$ .
[2 marks]
Answer $\dots$ m³

Example 3

A cylinder has a volume of $500$ cm³ and a radius of $5$ cm. Work out its height $h$ , to $3$ s.f.

Not drawn accurately

Hint

500 = π \times 5^{2} \times h

. Divide

500

by the area of the end.

B3
A cylinder has a volume of $1200$ cm³ and a radius of $7$ cm. Work out its height $h$ , to $1$ d.p.
[3 marks]
Not drawn accurately
Answer $h = \dots$ cm

Example 4

A cylinder has a volume of $900$ cm³ and a height of $14$ cm. Work out its radius $r$ , to $1$ d.p.

Not drawn accurately

Hint

900 = π r^{2} \times 14

. Find

r^{2}

first, then take the square root.

B4
A water tank is a cylinder with a volume of $2.5$ m³ and a height of $1.6$ m. Work out its diameter $d$ , to $3$ s.f.
[3 marks]
Not drawn accurately
Answer $d = \dots$ m

Practice

Year 8

C1
A tin of soup has a diameter of $7.4$ cm and a height of $11$ cm. Work out its volume, to the nearest cm³.
[2 marks]
Answer $\dots$ cm³
C2
A coin has a diameter of $2.2$ cm and is $3$ mm thick. Work out its volume in cm³, to $2$ d.p.
[2 marks]
Answer $\dots$ cm³

C3
A vase is a cylinder with an inside radius of $6$ cm and an inside height of $28$ cm. It is two-thirds full of water. How many litres of water are in it? Give your answer to $2$ d.p.
[3 marks]
Answer $\dots$ litres
C4
A copper rod is a cylinder with a diameter of $1.6$ cm and a length of $30$ cm. $1$ cm³ of copper has a mass of $8.9$ g. Work out the mass of the rod, to the nearest gram.
[3 marks]
Answer $\dots$ g
C5
The volume of a cone is $\frac{1}{3} π r^{2} h$ . Work out the volume of this cone, to $3$ s.f.
[2 marks]
Answer $\dots$ cm³

Exam-style questions

GCSE Foundation

D1
Sam says, "If you double the radius of a cylinder and keep its height the same, its volume doubles."
Use this cylinder to show that Sam is wrong.
[3 marks]

D2
A jug is a cylinder of radius $8$ cm and height $20$ cm. It is full of juice. The juice is poured into glasses. Each glass is a cylinder of radius $3.5$ cm and height $9$ cm. How many glasses can be filled completely?
[4 marks]
Answer $\dots$ glasses
D3
A metal pipe is $2.5$ m long. The end of the pipe is shown. It has an outside diameter of $12$ cm and an inside diameter of $9$ cm.
(a)
Work out the volume of metal in the pipe, in cm³, to $3$ s.f.
[3 marks]
Answer $\dots$ cm³
(b)
$1$ cm³ of the metal has a mass of $7.8$ g. Work out the mass of the pipe in kg, to $1$ d.p.
[2 marks]
Answer $\dots$ kg
Total for D3: 5 marks
D4
Cylinder $A$ has a radius of $10$ cm. It holds water to a depth of $18$ cm. All the water is poured into the empty cylinder $B$ , which has a radius of $15$ cm.
(a)
Work out the volume of the water, in terms of $π$ .
[1 mark]
Answer $\dots$ cm³
(b)
Work out the depth of the water in cylinder $B$ .
[3 marks]
Answer $\dots$ cm
Total for D4: 4 marks

Extension

Stretch

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

E1
Cylinder $A$ has a radius of $6$ cm and a height of $10$ cm. Cylinder $B$ has the same volume as $A$ , and its height is $2.5$ times its radius. Work out the radius of $B$ , to $3$ s.f.
[4 marks]
Not drawn accurately
Hint 1 · What to try
The volume of $A$ is $π \times 6^{2} \times 10 = 360 π$ cm³.
Hint 2 · The first line
For $B$ , $V = π \times r^{2} \times 2.5 r = 2.5 π r^{3}$ .
Hint 3 · The full method
$2.5 π r^{3} = 360 π$ , so $r^{3} = 144$ and $r = 3144 = 5.24$ cm.
Answer $r = \dots$ cm

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can find the volume of a cylinder with $V = π r^{2} h$ .
I can give a volume in terms of $π$ .
I can find the height or the radius from the volume.
I can use volumes to answer questions about capacity and mass.

Answers and mark scheme

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.

Get the answers