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 (a) 1 unit (b) units (c) unit (d) unit

Options

A. 1
B. 2
C. 0.5
D. none of these

Answer

B

Explanation

`V=(4)/(3)pir^(3)`
`therefore" "(dV)/(dt)=(4)/(3)pi.3r^(2)(dr)/(dt)`
Given `(dV)/(dt)=(dr)/(dt)`
`therefore" "r^(2)=(1)/(4pi) rArr r=(1)/(2sqrtpi)`
`therefore" "k=2`