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Find the area of the sector of a circle when the angle of the sector is 63∘ and the diameter of the circle is 20 cm.

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35 cm2

45 cm2

55 cm2

65 cm2

answer is C.

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Detailed Solution

First we will draw the circle showing the sector.

https://www.vedantu.com/question-sets/cfe839f7-aef4-4d86-bfe5-d593139108201295439612590117367.png

We will find the radius of the circle.
Substituting 20 for diameter in d = 2r, we get
20 = 2r
⇒10 = r
The radius of the circle is 10 cm.
We will now find the area of the given sector.
By substituting 63∘ for θ, 10 for r and

\frac{22}{7}

for π in the formula

A = π r^{2} \frac{θ}{360}

, we get

\Rightarrow A = \frac{22}{7} \times {(10)}^{2} \times \frac{63}{360}

Simplifying the expression, we get

\Rightarrow A = \frac{22 \times 100}{40}

\Rightarrow A = 55 c m^{2}

∴ Option 3 is the correct option.

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