Question

The area of a sector of a circle is 38.5cm³. find the radius of the circle if the angle substended at the center is 90° . ( Take π=22/7)

Answer 1

To find the radius of the circle given that the area of a sector is \(38.5 \, \text{cm}^2\) and the angle subtended at the center is \(90^\circ\), we can use the formula for the area of a sector:

\[
\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.

Given:
- \(\text{Area} = 38.5 \, \text{cm}^2\)
- \(\theta = 90^\circ\)
- \(\pi = \frac{22}{7}\)

Substituting the values into the formula:

\[
38.5 = \frac{90}{360} \times \frac{22}{7} \times r^2
\]

Simplifying \(\frac{90}{360} = \frac{1}{4}\):

\[
38.5 = \frac{1}{4} \times \frac{22}{7} \times r^2
\]

Multiplying both sides by 4:

\[
154 = \frac{22}{7} \times r^2
\]

Now, multiplying both sides by \(7\) to eliminate the fraction:

\[
154 \times 7 = 22 \times r^2
\]

Calculating \(154 \times 7\):

\[
1078 = 22 \times r^2
\]

Dividing both sides by \(22\):

\[
r^2 = \frac{1078}{22}
\]

Calculating \(\frac{1078}{22}\):

\[
r^2 = 49
\]

Taking the square root of both sides gives:

\[
r = \sqrt{49} = 7
\]

Therefore, the radius of the circle is

\[
\boxed{7 \, \text{cm}}
\]