Question

The circumference of a circle exceeds its diameter by $30cm$. Find the radius of the circle.

Answer 1

Let the radius of the given circle be $rcm$
Then, its circumference $=2\pi r$
Given:
(Circumference) $-$(Diameter) $=30cm$
$\Rightarrow (2\pi r-2r)=30$
$\Rightarrow 2r(\pi -1)=30$
$\Rightarrow r=\frac{30}{(\pi -1)2}$
$\Rightarrow r=\frac{30}{(\frac{22}{7}-1)2}$
$\Rightarrow r=\frac{15}{\left(\frac{15}{7}\right)}$
$\Rightarrow r=15\times \frac{7}{15}$
$\therefore r=7cm$
Hence, the radius of the given circle $=7cm$