KS3 Maths · Year 7 · Chapter 14: Circles · Lesson 3

Formula for the area of a circle

Year 7About 75 minutesCalculator allowed46 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $3. 5^{2}$ .
[1 mark]
Answer
A2
Last lesson
A circle has a diameter of $11$ cm. Work out its circumference to $1$ decimal place.
[1 mark]
Answer
A3
Needed today
Work out the area of a rectangle $7.5$ cm long and $4$ cm wide.
[1 mark]
Answer
A4
From chapter 1
Work out $196$ .
[1 mark]
Answer

Example, then your turn

Year 7

Use the $π$ key on your calculator. Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the area of the circle. Give your answer to $1$ decimal place.

Hint

A = π r^{2}

. Square the radius first, then multiply by

π

B1
Work out the area of the circle. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ m²

Example 2

Work out the area of the circle. Give your answer to $1$ decimal place.

Hint The line across the circle is a diameter. Halve it to get the radius.

B2
Work out the area of the circle. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ mm²

Example 3

A circle has a radius of $11$ cm. Work out its area. Give your answer in terms of $π$ .

Hint "In terms of

π

" means leave

π

in the answer. Do not multiply it out.

B3
Work out the area of each circle. Give your answers in terms of $π$ . (a) A circle with radius $9$ cm. (b) A circle with diameter $30$ cm.
[2 marks]

Example 4

Work out the area of the semicircle. Give your answer to $1$ decimal place.

Hint A semicircle is half of a circle. Work out the area of the whole circle, then halve it.

B4
The shape is a quarter of a circle. Work out its area. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ cm²

Example 5

The area of a circle is $50$ cm². Work out its radius. Give your answer to $1$ decimal place.

Hint

π r^{2} = 50

, so

r^{2} = 50 \div π

. Then take the square root.

B5
The area of a circle is $120$ m². Work out its radius. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ m

Practice

Year 7

C1
A circle of radius $5$ cm is cut into $8$ equal sectors. They are laid side by side to make a shape close to a rectangle. The long side is half of the circumference. The short side is the radius. Work out the long side and the area, each to $1$ decimal place.
[3 marks]
C2
The shaded shape is a ring between two circles with the same centre. The radii are $12$ cm and $5$ cm. Work out the area of the ring. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm²

C3
A circle fits exactly inside a square of side $20$ cm. Work out the total area of the four shaded corners. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm²
C4
A circular pond has a diameter of $9.4$ m. Work out the area of the pond to the nearest square metre.
[2 marks]
Answer $\dots$ m²

Exam-style questions

GCSE Foundation

D1
Lily works out the area of a circle with diameter $26$ cm. She writes: $π \times 2 6^{2} = 2123.7$ cm².
Explain Lily's mistake. Work out the correct area to $1$ decimal place.
[3 marks]

D2
A small pizza has a diameter of $20$ cm and costs £ $6$ . A large pizza has a diameter of $30$ cm and costs £ $12$ . Which pizza gives more pizza for each pound? You must show your working.
[5 marks]
D3
A lawn is a rectangle $12$ m by $8$ m with a semicircle on one $8$ m side.
Not drawn accurately
(a)
Work out the area of the lawn. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ m²
(b)
One box of grass seed covers $25$ m². How many boxes are needed to cover the lawn?
[2 marks]
Answer
Total for D3: 5 marks
D4
A café has $6$ round table tops, each with a radius of $0.6$ m. Each top needs $2$ coats of varnish. One tin of varnish covers $3$ m². How many tins are needed? You must show your working.
[4 marks]
Answer $\dots$ tins

Extension

Stretch

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

E1
Two square sheets of card each have side $24$ cm. From sheet $A$ one circle is cut, as large as possible. From sheet $B$ four equal circles are cut, as large as possible. Which sheet has more card left over? Give the area left on each sheet to $1$ decimal place.
[3 marks]
Hint 1 · What to try
On sheet $A$ the circle has radius $12$ cm. On sheet $B$ each circle has radius $6$ cm.
Hint 2 · The first line
Area of the square: $24 \times 24 = 576$ . Take away the circles on each sheet.
Hint 3 · The full method
$A$ : $576 - π \times 1 2^{2} = 123.6$ . $B$ : $576 - 4 \times π \times 6^{2} = 123.6$ . They are the same.
Answer $\dots$ cm² and $\dots$ cm²

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use $A = π r^{2}$ to work out the area of a circle.
I can work out an area from a diameter, or leave it in terms of $π$ .
I can work out the area of a semicircle, a ring or a compound shape.
I can work out a radius from an area.

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