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

A. 25%

B. 50%

C. 75%

D. 100%

Solution:

Let original radius be R cm
Then, original circumference =

2 π r

cm
New radius :

\begin{aligned} = (175 % of R) c m \\ = (\frac{175}{100} \times R) c m \\ = \frac{7 R}{4} c m \end{aligned}

New circumference :

\begin{aligned} = (2 π \times \frac{7 R}{4}) c m \\ = \frac{7 π R}{2} c m \end{aligned}

Increase in circumference :

\begin{aligned} = (\frac{7 π R}{2} - 2 π R) c m \\ = \frac{3 π R}{2} c m \end{aligned}

Increase % :

\begin{aligned} = (\frac{3 π R}{2} \times \frac{1}{2 π R} \times 100) % \\ = 75 % \end{aligned}

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