Question

If the length of a circular arc is 10$cm$ and radius is 3.5$cm$ Find the area of the minor sector and find the area of a major sector of the circle.

Answer 1

Radius of circle $3.5cm$

Length of circular is given by $\frac{x}{360}\times 2\pi r=10$
$=\frac{x}{360}\times 2\times \frac{22}{7}\times 3.5=10$
$=\frac{x}{360}=\frac{10}{22}\cdots 1$

Area of the sector is given by $\frac{x}{360}\times \pi r^2$

$=\frac{10}{22}\times \frac{22}{7}\times 3.5\times 3.5$
$=5\times 3.5$$=17.5c{m}^2$

Area of circle is $\pi r^2=\frac{22}{7}\times 3.5\times 3.5$$=38.5c{m}^2$

Area of major sector is $38.5-17.5c{m}^2=21c{m}^2$