Question:

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

Updated On: Nov 2, 2023
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Solution and Explanation

Find the area of a quadrant of a circle whose circumference is 22cm.
Let the radius of the circle be rr.
circumference = 22cm22cm
2πr2πr = 2222
 rr = 222π\frac{22}{ 2π} = 11 π\frac{11}{ π}

 Quadrant of circle will substend 90°90^{\degree}angle at the centre of the circle.

Area of such quadrant of the circle = 90°360°× πr2\frac{90^{\degree}}{ 360^{\degree} }\times π r^2

14× π×(11π)2\frac{1}{ 4} \times π \times (\frac{11}{π})^2

1214π\frac{121}{ 4π }121×74×22\frac{121 \times 7 }{ 4 \times 22}

778cm2\frac{77}{8} cm^2

Therefore, area of a quadrant of a circle is 778cm2\frac{77}{8} cm^2.

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