The central angle of a sector of a circle is $45^{\circ }$ and the radius of the circle is $14\text{ cm}$. Find (i) the length of the arc of the sector, and (ii) the area of the sector. Give your answers in cm and cm${}^2$ respectively, correct to two decimal places.

Step-by-step solution

1. The sector occupies a fraction $\frac{45}{360}=\frac{1}{8}$ of the whole circle.
2. Arc length $=\frac{1}{8}\times 2\pi r=\frac{1}{8}\times 2\pi \times 14=3.5\pi \text{ cm}\approx 11.00\text{ cm}$.
3. Area $=\frac{1}{8}\times \pi r^2=\frac{1}{8}\times \pi \times 14^2=24.5\pi {\text{ cm}}^2\approx 77.00{\text{ cm}}^2$.

Concept tested: Sector area and arc length

Published 20 August 2026 · How this solution was prepared and checked