Question

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.

Answer 1

Let the radius of the third circle be R.
Area of the circle with radius $R=\pi R^2$
Area of the circle with radius $8cm=\pi \times 8^2=64\pi c{m}^2$
Area of the circle with radius $6cm=\pi \times 6^2=36\pi c{m}^2$
Sum of the area of two circles $=64\pi c{m}^2+36\pi c{m}^2=100\pi c{m}^2$
Area of the third circle $=\pi R^2=100\pi c{m}^2$
$\Rightarrow \pi R^2=100\pi c{m}^2$
$\Rightarrow R^2=100c{m}^2$
$\Rightarrow R=10cm$
Thus, the radius of the new circle is 10 cm.