Find the radius of a circle whose area is equal to the sum of the areas of the two circles of radii $24\ cm$ and $7\ cm$ respectively.


Given: A circle whose area is equal to the sum of the areas of the two circles of radii $24\ cm$ and $7\ cm$ respectively.

To do: To find the radius of the circle.

Solution:

The radius of circles is $r_1=7\ cm,\ r_2=24\ cm$

Area of smaller circle is $A_1=\pi r_{1}^2$

$\Rightarrow A_1=\pi \times 7^2$

$\Rightarrow A_1=49\pi $

Area of Larger circle is $A-2=\pi r_{2}^2$

$\Rightarrow A_2=\pi \times 24^2$

$\Rightarrow A_2=576\pi $

Let $r$ be the radius of the required circle.

Area of required circle $A=\pi r^2$

As given, $A=A_1+A_2$

$\Rightarrow \pi r^2=576\pi +49\pi$

$\Rightarrow r^2=625$

$\Rightarrow r=\sqrt{625}$

$\Rightarrow r=25$

Radius of circle is $25\ cm$.

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Updated on: 10-Oct-2022

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