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Question
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.
Options
True
False
Solution
This statement is True.
Explanation:
Let the side of a cube be x
∴ Volume of a cube (Vc) = (x)3
Radius of a sphere `(r) = x/2`
Volume of sphere `(V_s) = 4/3 pi(r^3)`
= `4/3 pi (x/2)^3`
= `4/3 pi xx x^3/8`
∴ `V_c/V_s = x^3/(4/3 pi x^3/8) = 6/pi` or 6 : π
Hence, the required ratio is 6 : π.
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