Discussion Forum

If the radius of a circle is increased by 75%, then its circumference will increase by :

Answer:

Explanation:

Let original radius be $R$ cm. Then, original circumference $=2\pi R$ cm.

New radius = ($175\%$ of $R$)cm $=\left(\frac{175}{100}\times R\right)$ cm $=\frac{7R}{4}$ cm.

New circumference $=\left(2\pi\times\frac{7R}{4}\right)$ cm $=\frac{7\pi R}{2}$ cm.

Increase in circumference $=\left(\frac{7\pi R}{2}-2\pi R\right)$ cm $=\frac{3\pi R}{2}$ cm.

Increase % $=\left(\frac{3\pi R}{2}\times\frac{1}{2\pi R}\times 100\right)$% = 75%.