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The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its 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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