Question

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

Answer 1

Let the radius of the circle be \(r\).
The circumference is \(22cm\).
Therefore, \(2πr = 22\).
Solving for \(r\), we get \(r = \frac{22}{2π} = \frac{11}{π}\).

A quadrant of a circle subtends an angle of \(90^{\degree}\) at the center.

The area of such a quadrant is given by \(\frac{90^{\degree}}{360^{\degree}} \times π r^2\).

Substituting the value of \(r\), the area is \(\frac{1}{4} \times π \times (\frac{11}{π})^2\).

This simplifies to \(\frac{121}{4π}\). To calculate a numerical value, we substitute \(π \approx \frac{22}{7}\), giving \(\frac{121 \times 7}{4 \times 22}\).

The final area is \(\frac{77}{8} cm^2\).

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