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

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

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

A sector has radius $r=3 \text{ cm}$ and area $30\pi\text{ cm}^2$. Find its central angle $\theta$ in degrees.

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

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

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

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

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

Given a sector with radius $5x\text{ cm}$ and central angle $\tfrac{\pi}{3}\text{ rad}$ has area $\dfrac{25\pi x^2}{6}\text{ cm}^2$. Verify this area.

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

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 $\tfrac{16\pi}{3}\text{ m}^2$, radius $r=2x+1\text{ m}$ and angle $\theta=\tfrac{(x+2)\pi}{6}\text{ rad}$, find $x$.