Questions: A sector of a circle has a central angle of 60°. Find the area of the sector if the radius of the circle is 15 cm.

Find the area of the sector of a circle with a central angle of \(60^{\circ}\) and a radius of 15 cm.

Formula for the area of a sector

The area \(A\) of a sector with central angle \(\theta\) (in degrees) and radius \(r\) is given by:
\[ A = \frac{\theta}{360} \cdot \pi r^2 \]

Substitute the given values

Given: \(\theta = 60^{\circ}\), \(r = 15 \, \text{cm}\). Substitute these into the formula:
\[ A = \frac{60}{360} \cdot \pi \cdot (15)^2 \]

Simplify the expression

First, simplify \(\frac{60}{360}\):
\[ \frac{60}{360} = \frac{1}{6} \]
Next, calculate \(15^2\):
\[ 15^2 = 225 \]
Now, substitute these values back into the equation:
\[ A = \frac{1}{6} \cdot \pi \cdot 225 \]

Calculate the area

Multiply the values:
\[ A = \frac{225}{6} \cdot \pi = 37.5 \cdot \pi \]
Thus, the area of the sector is:
\[ A = 37.5\pi \, \text{cm}^2 \]

The area of the sector is \(\boxed{37.5\pi \, \text{cm}^2}\).

The area of the sector is \(\boxed{37.5\pi \, \text{cm}^2}\).