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 10 - 2020 - Paper 2

Question 10

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. Wo... show full transcript

Worked Solution & Example Answer:The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 10 - 2020 - Paper 2

Step 1

Work out the length of CB

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Answer

To find the length of radius CB, we can use the Pythagorean theorem, as triangle ABC is a right-angled triangle.

Using the formula: $a^2 + b^2 = c^2$ where (a = 6 \text{ m} ) and (b = 9 \text{ m} ), the length of CB (hypotenuse) will be:

$CB = \sqrt{(6^2 + 9^2)} = \sqrt{36 + 81} = \sqrt{117} \approx 10.817 \text{ m}$

Step 2

Calculate the area of the quarter circle

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Answer

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

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

Substituting the radius we found:

$\text{Area} = \frac{1}{4} \pi (10.817)^2 \approx \frac{1}{4} \pi (116.939) \approx 92.201 \text{ m}^2$

Finally, rounding to 3 significant figures, the area is approximately:

(92.2 ext{ m}^2)

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