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12. OAB is a sector of a circle with centre O and radius 7 cm - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 2

Question 13

12. OAB is a sector of a circle with centre O and radius 7 cm. The area of the sector is 40 cm². Calculate the perimeter of the sector. Give your answer correct to... show full transcript

Worked Solution & Example Answer:12. OAB is a sector of a circle with centre O and radius 7 cm - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 2

Step 1

Calculate the size of the angle

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Answer

To find the angle of the sector, we will use the formula for the area of a sector:

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

Substituting the known values:

$40 = \frac{\theta}{360} \times \pi (7)^2$

Solving for ( \theta ):

$40 = \frac{\theta}{360} \times 49\pi$

$\theta = \frac{40 \times 360}{49\pi}$

Calculating this gives ( \theta \approx 94.44^{\circ} ).

Step 2

Calculate the arc length

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Answer

The formula for the arc length (L) of a sector is:

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

Substituting ( \theta ) and ( r ):

$L = \frac{94.44}{360} \times 2\pi (7)$

Calculating this gives:

$L \approx 10.93 \text{ cm}$ .

Step 3

Calculate the perimeter of the sector

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Answer

The perimeter (P) of the sector is the sum of the lengths of the two radii and the arc length:

$P = 2r + L$

Substituting values:

$P = 2(7) + 10.93$

Calculating gives:

$P \approx 24.93 \text{ cm}$ .

Rounding to 3 significant figures, the answer is:

$P = 24.9 \text{ cm}$ .

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