IB Mathematics Applications & Interpretation 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 $r$.