Question

If the radius of a sphere becomes 3 times, then its volume will become ______.

Options

• 3 times

• 6 times

• 9 times

• 27 times

Answer 1

If the radius of a sphere becomes 3 times, then its volume will become 27 times.

Explanation:

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