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=3.2π cm2
upper A equals 3.2 pi cm squared

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

A=204.8π cm2

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,
- \( \theta = 72^\circ \).

Substituting the values into the formula:

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

Calculating this step by step:

1. Calculate \((16)^2\):

\[
(16)^2 = 256
\]

2. Substitute back into the equation:

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

3. Simplify \(\frac{72}{360}\):

\[
\frac{72}{360} = \frac{1}{5}
\]

4. Now substitute that into the area equation:

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

5. Calculate \(\frac{256}{5}\):

\[
\frac{256}{5} = 51.2
\]

6. Finally, substitute back to find \( A \):

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

So, the area of the sector is:

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

Therefore, the correct response is: **A=51.2π cm²**.