Edexcel IGCSE Math A 4.9.E circumference and area of circles

Practise circle-measure questions by choosing the radius or diameter, applying the correct formula and rounding to the stated accuracy.

Exam points

Calculate circumference or area from a given radius or diameter using circle formulae.
Find shaded areas involving circles inside squares or combined circle diagrams.
Use sector area or arc information when a circle part is shown in the diagram.

[Maximum number: 4]

The diagram shows the design for a badge, which will be made using wire. The design is a circle inside a square ABCD

The circle touches the square at the points E, F, G and H
The area of the square is $81 \mathrm{~cm}^{2}$
Calculate the total length of wire that will be needed to make the square and the circle.
Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn Diagram NOT accurately drawn

Square side length:
$\sqrt{81}=9$

Perimeter of the square:
$4\times9=36$

Circumference of the circle:
$\pi\times9=28.2743\ldots$

Total wire length:
$36+28.2743\ldots=64.2743\ldots$

Final answer:
$64.3\text{ cm}$

Accept 64.26 to 64.3.

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4.9.E Circumferences and areas of circles using relevant question 1