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Question
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
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Solution
Let the radius of two sphere number is r1 and r2.
∵ `r_1/r_2 = 1/3`
Volumes of spheres,
V1 = `4/3 πr_1^3`
and V2 = `4/3 πr_2^3`
Now,
`V_1/V_2 = (r_1^3)/(r_2^3) = (r_1/r_2)^3`
`= (1/3)^3 = 1/27`
∴ V1 : V2 = 1: 27
Hence, the volume of two spheres are in the ratio of 1: 27.
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