Question

The area of a sector is 22cm. What is the radius of the sector if the angle subtended at the centre is 140 degree

Answer 1

To find the radius of the sector given the area and the angle subtended at the center, you can use the formula for the area of a sector:

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

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

Given:
- Area of the sector = 22 cm²
- \(\theta = 140\) degrees

Now, we can rearrange the formula to solve for \(r\):

1. Substitute the values into the formula:

\[
22 = \frac{140}{360} \times \pi r^2
\]

2. Simplify \(\frac{140}{360}\):

\[
\frac{140}{360} = \frac{7}{18}
\]

Now we have:

\[
22 = \frac{7}{18} \times \pi r^2
\]

3. To isolate \(r^2\), multiply both sides by \(\frac{18}{7}\):

\[
22 \times \frac{18}{7} = \pi r^2
\]

4. Calculate the left side:

\[
\frac{22 \times 18}{7} = \frac{396}{7} \approx 56.5714
\]

So:

\[
\pi r^2 = \frac{396}{7}
\]

5. Now, divide both sides by \(\pi\) to solve for \(r^2\):

\[
r^2 = \frac{396}{7\pi}
\]

6. Finally, take the square root to find \(r\):

\[
r = \sqrt{\frac{396}{7\pi}}
\]

Using \(\pi \approx 3.14159\):

\[
r \approx \sqrt{\frac{396}{7 \times 3.14159}} \approx \sqrt{\frac{396}{21.99193}} \approx \sqrt{18.0009} \approx 4.24 \text{ cm}
\]

Thus, the radius of the sector is approximately **4.24 cm**.