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AOB is a sector of a circle, centre O and radius 6 cm - OCR - GCSE Maths - Question 12 - 2018 - Paper 5

Question 12

AOB is a sector of a circle, centre O and radius 6 cm. The length of arc AB is 5 cm. Find the area of the sector. Give your answer in terms of π.

Worked Solution & Example Answer:AOB is a sector of a circle, centre O and radius 6 cm - OCR - GCSE Maths - Question 12 - 2018 - Paper 5

Step 1

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Answer

The formula for the length of an arc is given by:

$L = \frac{\theta}{360} \times 2 \pi r$

Where:

Substituting the known values:

$5 = \frac{\theta}{360} \times 2 \pi \times 6$

Rearranging gives: $\theta = \frac{5 \times 360}{2 \pi \times 6}$

This simplifies to: $\theta = \frac{5 \times 360}{12 \pi} = \frac{150}{\pi}$

Step 2

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Answer

The area (A) of a sector is given by:

$A = \frac{\theta}{360} \times \pi r^2$

Substituting (\theta = \frac{150}{\pi}) and r = 6:

$A = \frac{150}{360} \times \pi \times (6)^2$

This simplifies to: $A = \frac{150}{360} \times \pi \times 36 = \frac{150 \times 36 \pi}{360}$

Reducing gives: $A = 15\pi$

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