Question

The diameters of the two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to the sum of the areas of the two given circle.

Answer 1

Let, $d$ be the diameter and $r$ be the radius of circle

For circle 1, $d_1=32cm$ $\Rightarrow r_1=16cm$

For circle 2, $d_2=24cm$ $\Rightarrow r_2=12cm$

Area of circle 1 $=\pi r_1^2=\pi (16{)}^2=256\pi$

Area of circle 2 $=\pi r_2^2=\pi (12{)}^2=144\pi$

It is given that,

Area of circle 3 = Area of circle 1 + Area of circle 2

Area of circle 3 $=256\pi +144\pi$

$\pi r_3^2=(256+144)\pi$ where $r_3$ is the radius of third circle

$r_3=\sqrt{256+144}$

$r_3=\sqrt{400}=20$

$r_3=20cm.$