Question

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle in cm having area equal to the sum of the areas of the two circles. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

The radii of the circles are 8 cm and 6 cm.

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

Area $=\pi \times 8\times 8=64\pi c{m}^2$

$=\pi \times 6\times 6=36\pi c{m}^2$

i.e., the area of required circle is $64\pi +36\pi$
$=100\pi c{m}^2$

i.e., the radius of required circle is $=\sqrt{\frac{100\pi }{\pi }}$

$=10cm$