Question

The radii of two circles are 8 cm and 6 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is

• A. 10
• B. 14
• C. 20
• D. 28

Answer 1

The correct option is C

20

Let the radius of the required circle be r cm.

Area of required circle = area of circle of radius 8 cm + area of circle of radius 6 cm
$\Rightarrow \pi r^2=\pi (8cm{)}^2+\pi (6cm{)}^2$
$\Rightarrow r^2=64c{m}^2+36c{m}^2$
$\Rightarrow r^2=100c{m}^2$
$\Rightarrow r=10cm$

Thus, the diameter of the required circle is 2 $\times$ 10 cm = 20 cm.
The correct answer is C.