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Question
A sphere and a cube are of the same height. The ratio of their volumes is
Options
3 : 4
21 : 11
4 : 3
11 : 21
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Solution
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of the cube be x units.
So, volume of the sphere (V1) = `4/3 pi (d/2)^3`
`=4/3 pi (x/2)^3`
`=4/3 pi (x^3 /8)`
`= (pi x^3)/6`
Volume of the cube (V2) = S3
= x3
So, to find the ratio of the volumes,
`V_1/V-2 = (pi x^3/6)/x^3`
` = pi /6`
` = ((22/7))/6`
`=11/21 `
Therefore, the ratio of the volumes of sphere and cube of equal heights is 11 : 21.
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