Question

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.

Answer 1

Answer:

The area of the sector of the circle is 75π/2 or about 117.8097 square centimeters.

Step-by-step explanation:

Recall that the area of a sector of a circle is given by:

$\displaystyle A = \pi r^2 \cdot \frac{\theta ^\circ}{360^\circ}$

Where θ is the central angle, in degrees.

Since the central angle is 60° and the radius of the circle is 15 cm, the area of the sector will be:

$\displaystyle \begin{aligned} A &= \pi\left(15\right)^2 \cdot \frac{\left(60\right)^\circ}{360^\circ} \\ \\ &= \frac{225\pi}{6}\\ \\ &= \frac{75\pi}{2}\end{aligned}$

In conclusion, the area of the sector of the circle is 75π/2 or about 117.8097 square centimeters.