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:
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Correct answer: B
Explanation
The correct answer is option 2 i.e 1
A sphere is inserted into a cube then the side of the cube will be equal to diameter of the sphere.
⇒ s = 2r
Where 's' is the side of the cube and 'r' is the radius of the sphere.
⇒ a = s3 / (4 / 3)πr3
⇒ a = (2r)3 / (4 / 3)πr3
⇒ a =6 / π
And,
⇒ b = 4πr2 / 6s2
⇒ b = 4πr2 / 6(2r)2
⇒ b = π / 6
⇒ ab = (6 / π) × (π / 6) = 1