Question

Question 10
The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm abd 7 cm is
(A) 31 cm
(B) 25 cm
(C) 62 cm
(D) 50 cm

Answer 1

Let $r_1=24cm$ and $r_2=7cm$

$\therefore$ Area of first circle $=\pi r_1^2=\pi (24{)}^2=576\pi c{m}^2$

And area second circle $=\pi r_2^2=\pi (7{)}^2=49\pi c{m}^2$

According to the given condition,

Area of circle = Area of first circle + Area of second circle

$\therefore \pi R^2=576\pi +49\pi$ [ where R be radius of circle]

$\Rightarrow R^2=625\Rightarrow R=25cm$

$\therefore$ Diameter of a circle $=2R=2\times 25=50cm$