If the voume of a sphere is incereased by 8 times, then its radius will be increased by

Options

A. 2 times
B. 4 times
C. 6 times
D. 8 times

Explanation

Let the radius of the sphere be r units and its volume be V cubic-units.
`therefore V=(4)/(3)pir^(3)` (by formula)
Now,if the volume of the sphere be increased by 8 times, i.e., its volume be 8V cubic-units, then let its radius be `r_(1)` units.
`therefore 8V =(4)/(3)pir_(1)^(3) rArr 8xx(4)/(3)pir^(3) =(4)/(3)pir_(1)^(3) rArr r_(1)^(3)=8r^(3)`
`rArr r_(1)^(3)=(2r)^(3) rArr r_(1)=2r,` i.e., the radius will be increased by 2 times. Hence (a) is correct.