If the radius of a circle is increased by 75 | vedclass

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(C) The formula for the circumference of a circle is $C = 2 \pi r,$ where $r$ is the radius.Since $2 \pi$ is a constant,the circumference $C$ is direc

Vedclass · Accepted Answer

$75$

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(C) The formula for the circumference of a circle is $C = 2 \pi r,$ where $r$ is the radius.Since $2 \pi$ is a constant,the circumference $C$ is directly proportional to the radius $r$ $(C \propto r)$.If the radius $r$ is increased by $75 \%,$ the new radius $r'$ becomes $r + 0.75r = 1.75r$.The new circumference $C'$ will be $2 \pi (1.75r) = 1.75(2 \pi r) = 1.75C$.The percentage increase in circumference is given by $\frac{C' - C}{C} 	imes 100 = \frac{1.75C - C}{C} 	imes 100 = 0.75 	imes 100 = 75 \%$.Therefore,the circumference increases by $75 \%$.

If the radius of a circle is increased by $75 \%,$ then its circumference will increase by (in $\%$)

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