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

Find the area of a sector with radius $12 \text{ cm}$ and central angle $\frac{2\pi}{5} \text{ rad}$.

Find the radius of a circle if a sector of angle $2 \text{ rad}$ has area $200 \text{ cm}^2$.

A circle of radius $9$ cm has a sector with central angle $45^\circ$. Calculate the sector area to two decimal places.

A sector has radius $8$ cm and area $80 \, \text{cm}^2$. Calculate the central angle in radians.

The arc length of a sector is $10\pi$ cm and the radius is $10$ cm. Find the area of the sector.

Find the area of a sector of a circle with radius $10$ cm and central angle $60^\circ$.

The area of a sector is $50 \text{ cm}^2$ and its angle is $\frac{\pi}{2} \text{ rad}$. Find the radius of the circle.

A sector of a circle has radius $15 \text{ cm}$. If its area is $45\pi \text{ cm}^2$, find the central angle in radians.

A sector has radius $7 \text{ cm}$ and central angle $120^\circ$. Calculate its area.

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

The area of a sector is $18\pi \text{ cm}^2$ and its radius is $6 \text{ cm}$. Determine the central angle in radians.