Question 12 Marks
Find the area of a sector of a circle of radius 28cm and central angle 45°.
Answer
View full question & answer→Given that, Radius of a circle, r = 28cm
and measure of central angle $\theta=45^\circ$
Hence, the required area of a sector of a circle is 308cm
$\therefore$ Area of a sector of a circle $=\frac{\pi\text{r}^2}{360^\circ}\times\theta$
$\frac{22}{7}\times\frac{(28)^2}{360}\times45^\circ$
$=\frac{22\times28\times28}{7}\times\frac{45^\circ}{360^\circ}$
$=22\times4\times28\times\frac{1}{8}$
$=22\times14$
$=308\text{cm}^2$
and measure of central angle $\theta=45^\circ$
Hence, the required area of a sector of a circle is 308cm
$\therefore$ Area of a sector of a circle $=\frac{\pi\text{r}^2}{360^\circ}\times\theta$
$\frac{22}{7}\times\frac{(28)^2}{360}\times45^\circ$
$=\frac{22\times28\times28}{7}\times\frac{45^\circ}{360^\circ}$
$=22\times4\times28\times\frac{1}{8}$
$=22\times14$
$=308\text{cm}^2$