Find the surface area of a sphere when its volume is changing at the same rate as its radius.

Options

A. 1
B. `(1)/(2sqrt(pi))`
C. `4pi`
D. `(4pi)/(3)`

Answer

A

Explanation

At any time t, let V, S and r denote respectively the volume, surface area and radius of the sphere. Then,
`V=(4)/(3)pir^(3) and S=4pir^(2)`
`therefore (dV)/(dt)=(dr)/(dt)implies4pir^(2)(dr)/(dt)=(dr)/(dt)implies4pir^(2)=1impliesS=1`