Question

a circle has a radius off 16 cm. find the area of a sector if 0=72

Answer 1

To find the area of a sector of a circle, you can use the formula:

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

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

In your case, the radius \(r = 16 \, \text{cm}\) and the angle \(\theta = 72^\circ\).

Now, plug these values into the formula:

1. Calculate \(\pi r^2\):
\[
\pi r^2 = \pi \times (16)^2 = \pi \times 256
\]

2. Substitute into the area formula:
\[
\text{Area of Sector} = \frac{72}{360} \times \pi \times 256
\]

3. Simplify \(\frac{72}{360}\):
\[
\frac{72}{360} = \frac{1}{5} \quad \text{(since } 72 \div 72 = 1 \text{ and } 360 \div 72 = 5 \text{)}
\]

4. Now calculate the area:
\[
\text{Area of Sector} = \frac{1}{5} \times \pi \times 256 = \frac{256\pi}{5}
\]

5. For a numerical value, you can approximate \(\pi\) as 3.14:
\[
\text{Area of Sector} \approx \frac{256 \times 3.14}{5} = \frac{804.48}{5} \approx 160.896 \, \text{cm}^2
\]

So, the area of the sector is approximately \(160.9 \, \text{cm}^2\).