The diagram shows a right-angled triangle and a quarter circle. The right-angled triangle ABC has angle ABC = 90°. The quarter circle has centre C and radius CB. Work out the area of the quarter circle. Give your answer correct to 3 significant figures. You must show all your working.

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The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 7 - 2020 - Paper 2

Question 7

The diagram shows a right-angled triangle and a quarter circle. The right-angled triangle ABC has angle ABC = 90°. The quarter circle has centre C and radius CB. W... show full transcript

Worked Solution & Example Answer:The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 7 - 2020 - Paper 2

Step 1

Find the length of radius CB

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Answer

First, we need to find the length of CB, which is the radius of the quarter circle. In triangle ABC, we can use the Pythagorean theorem:

$CB = \sqrt{AC^2 + AB^2}$

Substituting the values:

$CB = \sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117} \approx 10.82 \text{ m}$

Step 2

Calculate the area of the quarter circle

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Answer

The area A of a quarter circle is given by the formula:

$A = \frac{1}{4} \pi r^2$

Substituting the value of r:

$A = \frac{1}{4} \pi (10.82)^2 \approx \frac{1}{4} \pi \times 116.99 \approx 92.23 \text{ m}^2$

Rounding the answer to three significant figures, we get:

$A \approx 92.2 \text{ m}^2$

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