A circle has radius $8\text{cm}$. Find the area of the sector subtended by a central angle of $120^{\circ }$. Use $\pi =\frac{22}{7}$ and give the answer in square centimeters, rounded to one decimal place.

Step-by-step solution

1. Step 1: Write the formula for the area of a sector: $A_{\text{sector}}=\frac{\theta }{360^{\circ }}\pi r^2$.
2. Step 2: Plug in the given values: $\theta =120^{\circ }$, $r=8\text{cm}$ and $\pi =\frac{22}{7}$.
3. Step 3: Compute the fraction $\frac{120}{360}=\frac{1}{3}$.
4. Step 4: Compute $r^2=8^2=64$.
5. Step 5: Substitute into the formula: $A_{\text{sector}}=\frac{1}{3}\times \frac{22}{7}\times 64$.
6. Step 6: Simplify: $\frac{22}{7}\times 64=\frac{22\times 64}{7}=\frac{1408}{7}=201.142857\dots$
7. Step 7: Multiply by $\frac{1}{3}$: $A_{\text{sector}}=\frac{201.142857}{3}=67.047619\dots$
8. Step 8: Round to one decimal place: $67.0{\text{cm}}^2$

Concept tested: Area of a sector

Published 7 October 2026 · How this solution was prepared and checked