Find the area of a sector of a circle whose radius is $8\text{ cm}$ and whose central angle is $75^{\circ }$.

Step-by-step solution

1. Area of a whole circle is $\pi r^2$; for $r=8\text{ cm}$, ${\text{Area}}_{\text{circle}}=\pi \times 8^2=64\pi {\text{ cm}}^2$.
2. A sector with central angle $\theta$ occupies $\theta /360$ of the whole circle.
3. Thus ${\text{Area}}_{\text{sector}}=\frac{75}{360}\times 64\pi$.
4. Simplify: $\frac{75}{360}=\frac{5}{24}$, so area $=\frac{5}{24}\times 64\pi =\frac{320}{24}\pi =\frac{40}{3}\pi$.
5. Numerically, $\frac{40}{3}\pi \approx 13.333\times 3.1416\approx 33.51{\text{ cm}}^2$.

Concept tested: Area of a sector

Published 25 August 2026 · How this solution was prepared and checked

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