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. $31cm$
• B. $25cm$
• C. $17cm$
• D. $28cm$

Answer 1

The correct option is B $25cm$

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 $⟹576\pi +49\pi$

$⟹625\pi$

Radius of circle is given by

$\sqrt{625}=25$