IB Mathematics Applications & Interpretation 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 $\frac{\pi }{3}$.

Find the value of $r$.

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

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

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

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

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?

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

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 $7\text{ cm}$ and area $28{\text{ cm}}^2$.

A sector has an area of $18\pi {\text{ cm}}^2$ and a radius of $6\text{ cm}$. Find its central angle in radians.

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