Question

The length of an arc of a a circle, subtending an angle of ${54}^{\circ }$ at the center
is $16.5cm$ .Calculate the radius , circumference and area of the circle .

Answer 1

if angle subtended at center is ${54}^{\circ }$ then length of the Arc = 16.5cm

so if angle subtended at center is $1^{\circ }$ then,

length of the arc $=\left(16.5/54\right)cm$

so if angle subtended at center is 360${}^{\circ }$ (full circle),then length of ARC

that is circumference $=\left(16.5/54\right)\times {360}^{\circ }$

$=110cm$

so circumference =2$\pi r$

$\therefore 110=2\pi r$

$\therefore r=\frac{(110\times 7)}{2\times 22}=17.5cm$

so radius$=17.5cm$ area of circle = $\pi r^2$ =$\frac{22}{7}\times (17.5{)}^2=962.5c{m}^2$

hence,radius $=17.5cm$

circumference $=110cm$ and

area $=962.5c{m}^2$