If the rate of change in volume of spherical soap bubble is uniform then the rate of change of surface area varies as

Options

A. square of radius
B. square root of radius
C. inversely proportional to radius
D. cube of the radius

Answer

C

Explanation

Let volume =`V=4/3 pi r^(3)`
and surface are =`s = 4pi r^(2)`
`=4pi r^(2)(dr)/(dt)`
`rarr(ds)/(dt)=4 pi xx2xxr(dr)/(dt)=(8pi r^(2))/(r )(dr)/(dt)` ltrbgt `(2)/(r)[4pi r^(2)(dr)/(dt)]=(2)/(r ) (dv)/(dt)`