A sphere is placed in a cube so that it touches all the faces of the cube. If 'a' is the ratio of the volume of the cube to the v…

Question

A sphere is placed in a cube so that it touches all the faces of the cube. If 'a' is the ratio of the volume of the cube to the volume of the sphere and 'b' is the ratio of the surface area of the sphere to the surface area of the cube, then the value of 'ab' is:

1. A. pi^2/30
2. B. 4
3. C. 36/pi^2
4. D. 1 (Correct answer)

Correct Answer

Option D — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• Side = s, sphere radius = s/2. a = s^3/(pi*s^3/6) = 6/pi. b = pi*s^2/(6s^2) = pi/6. ab = (6/pi)(pi/6) = 1.