Question

The circumference of a circle is $123.2cm$.
Calculate :
(i) the radius of the circle in $cm;$
(ii) the area of the circle to the nearest $c{m}^2$;
(iii) the effect on the area of the circle when the radius is doubled.

Answer 1

A/Q $2\pi r=123.2cm$

$\Rightarrow 2\times 3.14\times r=123.2\Rightarrow r=\frac{123.2}{2\times 3.14}=\frac{61.6}{3.14}=19.61cm$

$\left(ii\right)$ area of circle $=\pi r^2=3.14\times (19.61{)}^{2}c{m}^2{A}_1=1207.49c{m}^2$

$\left(ii\right)$ Radius of new circle $=2\times 19.61cm=39.22cm$

$A_2,area=3.144\times (39.22{)}^{2}c{m}^2=4829.97c{m}^2\frac{A_2}{A_1}=\frac{4829.97c{m}^2}{1209.49c{m}^2}=4$