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Question
Choose the correct answer of the following question:
If the radius of a sphere becomes 3 times, then its volume will become
Options
3 times
6 times
9 times
27 times
Solution
Let the radius of the given sphere and that of the new sphere be r and R, respectively;
Also, the volume of the given sphere and that the new sphere be v and V,
We have,
R = 3r .........(i)
Now,
`"Volume of the new sphere"/"Volume of the given sphere" = ((4/3 pi"R"^3))/((4/3 pi"r"^3))`
`= ("R"/r)`
`= ((3r)/r)^3` [Using (i)]
= 33
= 27
Hence, the correct answer is option (d).
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