A spherical balloon is expanding. If the radius is increasing at the rate of `2 "cm min"^(-1)`, the rate at which the volume increases in cubic centrimeters per minute when theradius is 5 cm is

Options

A. `10 picm^(3) min^(-1)`
B. `100pi cm^(3) min^(-1)`
C. `200 pi cm^(3) min^(-1)`
D. `50 pi cm^(3)min^(-1)`

Answer

C

Explanation

Let volume of sphere `V=4/3pir^(3)`
`implies(dV)/(dt)=4 pir^(2)(dr)/(dt)=4pir^(2).(2)[ :' (dr)/(dt)=2]`
`:.(dV)/(dt)=8pi (5)^(2)=200pi cm^(3) min^(-1) [:' r=5cm]`