Question Type 3: Calculating the area of a sector given parameters Exercises

A sector has radius $r = 3\text{ cm}$ and area $3\pi\text{ cm}^2$. Find its central angle $\theta$ in degrees.

A sector with radius $r = 6\text{ cm}$ has area $4\pi\text{ cm}^2$. Find the central angle $\theta$ in radians.

Find the radius of a sector when its area is $18\text{ cm}^2$ and $\theta=\frac{\pi}{2}\text{ rad}$.

The area of a sector is $12\text{ m}^2$, its radius is $4x\text{ m}$ and its central angle is $3x\text{ rad}$. Find $x$.

Given a sector area of $\frac{16\pi}{3}\text{ m}^2$, radius $r=2x+1\text{ m}$ and angle $\theta=\frac{(x+2)\pi}{6}\text{ rad}$, find the value of $x$.

Calculate the area of a sector with radius $r = 5\text{ cm}$ and central angle $\theta = 60^\circ$.

The area of a sector is $22\pi \text{ m}^2$ when the central angle $\theta = 90^\circ$. Find the radius $r$ of the sector.

A sector has radius $r=7\text{ m}$ and area $x\pi\text{ m}^2$. Express the central angle $\theta$ in radians.

A sector has a radius of $5x\text{ cm}$ and a central angle of $\frac{\pi}{3}\text{ radians}$. Show that the area of the sector is $\frac{25\pi x^2}{6}\text{ cm}^2$.

A sector has radius $r=10\text{ cm}$ and central angle $2x$ degrees. If its area is $100\text{ cm}^2$, find $x$.

Find the area of a sector if $r=8 \text{ m}$ and $\theta=150^\circ$.

Given a sector area of $50 \text{ cm}^2$ and central angle $\theta=90^\circ$, find the radius $r$.