Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Given:

The circumference of a circle is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

To do:

We have to find the radius of the circle.

Solution:

Let the radius of the circle be $r$.

We know that,

Circumference of a circle of radius $r=2 \pi r$

Therefore,

The circumference of the circle of radius $15\ cm=2 \pi (15)$

$=30\pi$

The circumference of the circle of radius $18\ cm=2 \pi (18)$

$=36\pi$

According to the question,

$2\pi r=30\pi+36\pi$

$2\pi r=66\pi$

$r=33$

The radius of the circle is $33\ cm$.    

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Updated on: 10-Oct-2022

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