The difference between the circumferences of two circles is 132 cms. and the radius of smaller circle 14 cms. What is the radius of larger circle ?

The difference between the circumferences of two circles is 132 cms. and the radius of smaller circle 14 cms. What is the radius of larger circle ?
1). 14 cms.
2). 21 cms.
3). 30 cms.
4). 42 cms.

Solution

Let the radius of the larger circle be $R$ and the radius of smaller circle be $r$.
Given $r=14.$
$2\pi R - 2\pi r = 132$
$2\pi\left(R-r \right)=132$
$\pi\left(R-r \right)=66$
Consider $\pi = \frac{22}{7}$.
$R-14 = \frac{66\times7}{22}=21$
$R=21+14=35cms$.
Hence Option E is the correct answer.

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