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

Let S be the surface area and V be the volume of a sphere of radius r. Then,
`(dV)/(dt)=(dr)/(dt)" [Given]"`
`implies r=(1)/(2sqrt(pi))" [See illustration 2]"`
`therefore S=4 pir^(2)impliesS=1`