2D Area & Perimeter: WJEC GCSE Foundation June 2025 Unit 2 Q17

Foundation June 2025 Unit 2 Q17

17. The diagram below shows a sketch of a circle that fits exactly inside a square.

The radius of the circle is 5 cm.

Diagram not drawn to scale

Calculate the total area of the shaded regions.
Give your answer as a decimal.
You must show all your working. [4]

Total area of the shaded regions = …………………………

Mark scheme

Scheme	Marks	Comments
		Answers may be seen on diagram. Answer space takes precedence.
(Shaded area = ) \(10 \times 10 - \pi \times 5^2\)	M2	May be seen in stages. Award M1 for any one of the following: appropriate sight of 10 × 10 or equivalent area of square = 100 (cm²) appropriate sight of \(\pi \times 5^2\) or equivalent appropriate sight of \(25\pi\) 78·5 ≤ area of circle ≤ 78·55 (cm²)
21·4 ≤ shaded area ≤ 21·5 (cm²)	A2	FT ‘their 10’² – ‘their \(\pi \times 5^2\)’, provided that: \(\pi\) is used AND area of square > area of circle AND M1 awarded. Award A1 for one of the following: 78·5 ≤ area of circle ≤ 78·55 (cm²) \(100 - 25\pi\).

Scheme

Marks

Comments

Answers may be seen on diagram.
Answer space takes precedence.

(Shaded area = ) \(10 \times 10 - \pi \times 5^2\)

May be seen in stages.

Award M1 for any one of the following:

21·4 ≤ shaded area ≤ 21·5 (cm²)

FT ‘their 10’² – ‘their \(\pi \times 5^2\)’, provided that:

Award A1 for one of the following: