Question

Find the area of a sector in a circle with r=18cm and θ =60° . Round your answers to the nearest tenth.

Answer 1

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

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

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

In this case, \(r = 18 \, \text{cm}\) and \(\theta = 60^\circ\).

First, calculate the area of the entire circle:

\[
\text{Area of the circle} = \pi r^2 = \pi (18)^2 = \pi \times 324 = 324\pi \, \text{cm}^2
\]

Now, plug these values into the sector area formula:

\[
\text{Area of the sector} = \frac{60}{360} \times 324\pi
\]

Simplifying the fraction:

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

Now calculate the area of the sector:

\[
\text{Area of the sector} = \frac{1}{6} \times 324\pi = 54\pi \, \text{cm}^2
\]

Now, substitute \(\pi \approx 3.14\):

\[
\text{Area of the sector} \approx 54 \times 3.14 \approx 169.56 \, \text{cm}^2
\]

Rounding to the nearest tenth:

\[
\text{Area of the sector} \approx 169.6 \, \text{cm}^2
\]

Thus, the area of the sector is approximately **169.6 cm²**.