IB Mathematics Analysis and Approaches 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.