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Question
The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ______.
Options
9 : 16
16 : 9
3 : 4
4 : 3
Solution
The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is 16 : 9.
Explanation:
Let the radii of the spheres be and r.
Then ratio of their volumes
`= (4/3pi"R"^3)/(4/3pi"r"^3)`
Therefore,
`"V"_1/"V"_2 = (4/3pi"R"^3)/(4/3pi"r"^3) = 64/27`
`=> "R"^3/"r"^3 = 64/27`
`=> ("R"/"r")^3 = 64/27`
`=> ("R"/"r")^3 = (4/3)^3`
`= "R"/"r" = 4/3`
Hence, the ratio of their surface areas `= (4pi"R"^2)/(4pi"r"^2)`
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