The rate of change of volume of a sphere is equal to the rate of change of its radius, then its radius is equal to

Options

A. 1 unit
B. `sqrt(2pi)` units
C. `(1)/(sqrt(2pi))` unit
D. `(1)/(2sqrt(pi))`unit

Answer

D

Explanation

Let r be the radius and V be the volume of the sphere. Then,
`V=(4)/(3)pir^(3)`
`implies(dr)/(dt)=4pir^(2)(dr)/(dt)" "[because (dV)/(dt)=(dr)/(dt)"(given)"]`
`implies 4pir^(2)=1impliesr=(1)/(2sqrt(pi))`