Question

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

Answer 1

Let the radius of the circle be \(r\).
circumference = \(22cm\)
\(2πr\) = \(22\)
 \(r\) = \(\frac{22}{ 2π}\) = \(\frac{11}{ π}\)

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

Area of such quadrant of the circle = \(\frac{90^{\degree}}{ 360^{\degree} }\times π r^2\)

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

= \(\frac{121}{ 4π }\)= \(\frac{121 \times 7 }{ 4 \times 22}\)

= \(\frac{77}{8} cm^2\)

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