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# The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Given:

The radii of two circles are 8 cm and 6 cm respectively.

To do:

We have to find the radius of the circle having its area equal to the sum of the areas of the two circles.

Solution:

Let the radius of the circle be $r$.

We know that,

Area of a circle of radius $r=\pi r^2$

Therefore,

The area of the circle of radius $8\ cm=\pi (8)^2$

$=64\pi$

The area of the circle of radius $6\ cm=\pi (6)^2$

$=36\pi$

According to the question,

$\pi r^2=64\pi+36\pi$

$\pi r^2=100\pi$

$r^2=(10)^2$

$r=10$

The radius of the circle is $10\ cm$.

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