Question

If the radii of two circles re $7cm$ and $24cm$, then the radius of the circle having area equal to the sum of the areas of the two circles, is

• A. $25$
• B. $26$
• C. $27$
• D. $Noneofthese$

Answer 1

The correct option is A $25$

The radius of circles is $7cm,24cm$

Area of smaller circle is $\pi r^2$

$⟹\pi \times 7^2$

$⟹49\pi$

Area of Larger circle is $\pi r^2$

$⟹\pi \times {24}^2$

$⟹576\pi$

Area of required circle $⟹576\pi +49\pi =\pi r^2$

$⟹625\pi =\pi r^2$

$⟹625=r^2$

Radius of circle is given by

$\sqrt{625}=25$