Find the rate of change of radius of a sphere when its radius is `4 cm` and when its volume is changing at the rate of `(4pi)/(625)m^(3)//sec`

Options

A. `1m//s`
B. `2m//s`
C. `pim//s`
D. `3m//s`

Answer

A

Explanation

`V=(4)/(3)piR^(3)`
`(dV)/(dt)=4piR^(2)(dR)/(dt)`
`rArr(4pi)/(625)=4pi xx(4)/(100)xx(4)/(100)xx(dR)/(dt)`
`rArr(dR)/(dt)=1m//s`