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.

GCSE Edexcel Maths Simple & Compound Interest, Growth & Decay: The diagram shows a right-angled

The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 8 - 2020 - Paper 2

Question 8

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 8 - 2020 - Paper 2

Step 1

Find the length of CB

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Answer

Using the Pythagorean theorem, we need to find the third side of triangle ABC. The sides AB and AC are given as 9 m and 6 m respectively. Therefore,

$CB^2 = AB^2 + AC^2 = 9^2 + 6^2 = 81 + 36 = 117$

Thus,

$CB = ext{sqrt}(117) ext{ m}$ .

Step 2

Calculate the radius of the quarter circle

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Answer

From the previous calculation, we find that the radius of the quarter circle, which is the same as CB, is:

$CB ext{ (radius)} = ext{sqrt}(117) ext{ m} \approx 10.81565 ext{ m}$ (approximately).

Step 3

Work out the area of the quarter circle

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Answer

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

$A = rac{1}{4} imes ext{π} imes r^2$

Substituting the radius:

$A = rac{1}{4} imes ext{π} imes (CB)^2$

Hence, substituting CB:

$A = rac{1}{4} imes ext{π} imes (117) \approx 91.57 ext{ m}^2.$

Step 4

Final answer with significant figures

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Answer

To express the area correct to 3 significant figures:

The area of the quarter circle is approximately: $91.6 ext{ m}^2$ .

The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 8 - 2020 - Paper 2

Worked Solution & Example Answer:The diagram shows a right-angled triangle and a quarter circle - Edexcel - GCSE Maths - Question 8 - 2020 - Paper 2

Find the length of CB

Calculate the radius of the quarter circle

Work out the area of the quarter circle

Final answer with significant figures

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