Question

Question 3
Find the area of a sector of a circle of radius 28 cm and central angle ${45}^{\circ }$.

Answer 1

Given: Radius of a circle, r = 28 cm

Measure of central angle $\theta ={45}^{\circ }$

$\therefore$ Area of a sector of a circle $=\frac{\pi r^2}{{360}^{\circ }}\times \theta$

$=\frac{22}{7}\times \frac{(28{)}^2}{360}\times {45}^{\circ }$

$=\frac{22\times 28\times 28}{7}\times \frac{{45}^{\circ }}{{360}^{\circ }}$

$=22\times 4\times 28\times \frac{1}{8}$

$=22\times 14$

$=308c{m}^2$

Hence , the required area of the sector is $308c{m}^2$.