Question

The radius of a circle whose area is equal to the sum of the areas of two circles of radii are 5 cm and 12 cm is

• A. 13 cm
• B. 14 cm
• C. 15 cm
• D. none

Answer 1

The correct option is A 13 cm

Given two circle radii are $5cm$ and $12cm$

Then,

Area of circle of radius 5 cm $=$$\pi r^2=\pi (5{)}^2=25\pi$ sq cm

Area of circle of radius 12 cm $=$$\pi r^2=\pi (12{)}^2=144\pi$sq cm

So area of circle whose area is equal to sum of areas of two circles$=$$25\pi +144\pi =169\pi$ sq cm

Let the radius of the bigger circle be $=$R cm

$\therefore \pi R^2=169\pi$

$\Rightarrow R^2=169$

$\Rightarrow R=13cm$