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Question

Find the area of a quadrant of a circle whose circumference is 22cm.


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Solution

Step 1: Find the radius of the circle.

Given that, circumference of a circle is 22cm.

Suppose, radius of the circle be r, then circumference of the circle is 2πr.

Therefore, 2πr=22

2×227×r=22π227

447×r=22

r=22×744

r=72cm

Hence, radius of the circle is 72cm.

Step 2: Find the area of the circle.

Formula for finding area of a circle with radius r is πr2.

Radius =72cm

Area =π×722

=227×72×72

=772cm2

Hence, area of the circle is 772cm2.

Step 3: Find area of a quadrant.

Area of a quadrant =Area ×14

=772×14

=9.625cm2

Hence, the area of a quadrant of the circle is 9.625cm2.


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