Question

A circle has a radius of 16 cm. Find the area of a sector if θ=72°.(1 point)
Responses

A=51.2π cm2
upper A equals 51.2 pi cm squared

A=204.8π cm2
upper A equals 204.8 pi cm squared

A=3.2π cm2
upper A equals 3.2 pi cm squared

A=256π cm2
upper A equals 256 pi cm squared
Remaini

Answer 1

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

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

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

Given:
- \( r = 16 \) cm
- \( \theta = 72 \) degrees

Now, apply the values to the formula:

\[
A = \frac{72}{360} \times \pi \times (16)^2
\]

First, calculate \( (16)^2 \):

\[
(16)^2 = 256
\]

Now, substitute it into the area formula:

\[
A = \frac{72}{360} \times \pi \times 256
\]

Simplifying \( \frac{72}{360} \):

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

So now we have:

\[
A = \frac{1}{5} \times \pi \times 256
\]

This can be calculated as:

\[
A = \frac{256\pi}{5} = 51.2\pi \text{ cm}^2
\]

Thus, the area of the sector is:

\[
\boxed{51.2\pi \text{ cm}^2}
\]