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Question

Find the area of the sector of a circle if the radius of the circle is 5 cm, and the length of the arc is 4 cm.

A
10 cm2
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B
5 cm2
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C
20 cm2
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D
15 cm2
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Solution

The correct option is A 10 cm2
We know that,
Length of the arc(l)=θ360×2πr(i) where θ is the angle subtentded by the arc at the centre of the circle.

Area of the sector(A) = θ360×πr2
Multiply and divide with 2 on the R.H.S.
A=θ360×2πr2×12
A=(θ360×2πr)×r×12
A=l×r2 (from (i))

Given, l=4 cm,r=5 cm

Area of the sector(A)=4×52
=10

Hence, the area of the sector is 10 cm2.

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