Question:
The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is
(a) 31 cm
(b) 25 cm
(c) 62 cm
(d) 50 cm
Solution:
(d) Let r1 = 24 cm and r2 = 7 cm
$\therefore \quad$ Area of first circle $=\pi_{1}^{2}=\pi(24)^{2}=576 \pi \mathrm{cm}^{2}$
and area of second circle $=\pi r_{2}^{2}=\pi(7)^{2}=49 \pi \mathrm{cm}^{2}$
According to the given condition,
Area of circle $=$ Area of first circle $+$ Area of second circle
$\therefore \quad \pi R^{2}=576 \pi+49 \pi \quad$ [where, $R$ be radius of circle]
$\Rightarrow \quad R^{2}=625 \Rightarrow R=25 \mathrm{~cm}$
$\therefore \quad$ Diameter of a circle $=2 R=2 \times 25=50 \mathrm{~cm}$