Question

If the area of region bounded by the inscribed and circumscribed circles of a square is 9π, then the area of the square will be:

(a) 6π

(b) 5π

(c) 25

(d) 36

Answer 1

Correct option is (d) 36

Area of the circumscribed circle of a square is double the area of the circle inscribed in it.

Area of the inscribed circle = π\((\frac a2)^2 \) 

where, a = side of the square

\(\therefore 2\pi (\frac a2)^2 - \pi (\frac a2)^2 = 9 \pi\)

On solving we get, a = 6

∴ Area of the square = 6² = 36