Question

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24cm$ and $7cm$ is

• A. $31cm$
• B. $25cm$
• C. $62cm$
• D. $50cm$

Answer 1

Answer: (D)

$50cm$

Given:

The radii of the two circles are

$r_1=24cm\Rightarrow$ Area $A_1=\pi {r_1}^2=\pi {24}^2{cm}^2=576\pi {cm}^2$ and

$r_2=7cm\Rightarrow$ Area $A_2=\pi {r_2}^2=\pi 7^2{cm}^2=49\pi {cm}^2.$

$\therefore$ So $A_1+A_2=(576+49)\pi {cm}^2=625\pi {cm}^2.$

This is the area $A$ of the resulting circle.

$\therefore A=A_1+A_2=625\pi {cm}^2.$

Let the diameter of this circle be $d.$

Now the diameter of a circle $=2\sqrt{\frac{A}{\pi }}.$

$\therefore d=2\sqrt{\frac{625\pi }{\pi }}cm=50cm.$