Question Type 3: Calculating the area of sector given a radius and specific angle Exercises

Calculate the area of a sector with radius 5 cm and central angle $\frac{\pi}{3}$.

Compute the arc length of a sector with radius 10 m and angle $\frac{2\pi}{5}$.

A sector has area $18\pi$ cm$^2$ and radius 6 cm. Find its central angle in radians.

Given a circle of radius 8 cm, find the combined area of two sectors with angles $\frac{\pi}{6}$ and $\frac{\pi}{3}$.

Given a circle in which a sector’s radius doubles while its central angle stays $\frac{\pi}{3}$, by what factor does the sector area increase?

Find the radius of a circle if the arc length of a sector with angle $\frac{\pi}{4}$ is $5\pi$ cm.

Find the radius of a circle if the area of a sector with central angle $\frac{\pi}{2}$ is 50 cm$^2$.

Determine the central angle (in radians) of a sector with radius 7 cm and area 28 cm$^2$.

The area of a sector is half the area of the circle. Express the central angle in radians.

For a circle of radius $r$, the area of a sector equals its arc length. Find the angle in radians.

A sector has a perimeter (two radii plus arc) of $20+4\pi$ cm, with radius 4 cm. Find the central angle.

The area of a sector of a circle is 75 cm$^2$. If its arc length is 15 cm, find the radius and central angle.