Question

Central angle 60 degrees, radius 4cm, what is the area in cm squared

Answer 1

To find the area of a sector formed by a central angle in a circle, you can use the formula:

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

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

For your case:
- \(\theta = 60\) degrees,
- \(r = 4\) cm.

Plugging the values into the formula:

\[
\text{Area} = \frac{60}{360} \times \pi \times (4^2)
\]

Calculating \(4^2\):

\[
4^2 = 16
\]

Now substitute back into the area formula:

\[
\text{Area} = \frac{60}{360} \times \pi \times 16
\]

Simplifying \(\frac{60}{360}\):

\[
\frac{60}{360} = \frac{1}{6}
\]

Now, we substitute this into the area expression:

\[
\text{Area} = \frac{1}{6} \times \pi \times 16 = \frac{16\pi}{6} = \frac{8\pi}{3}
\]

Thus, the area of the sector is:

\[
\text{Area} \approx \frac{8 \times 3.14}{3} \approx \frac{25.12}{3} \approx 8.38 \text{ cm}^2
\]

So the exact area of the sector is \(\frac{8\pi}{3}\) cm², and approximately \(8.38\) cm².