The radius of a spherical ball is increasing at the rate of 1m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $36\pi \, m^3/sec$
$\frac{dR}{dt}=1m/sec$
$v=\frac{4}{3}πR^3$
$\frac{dv}{dt}=4πR^2\frac{dR}{dt}=4πR^2$
$\left.\frac{dv}{dt}\right]_{R=3}=4π×3^2$
$=36\pi \, m^3/sec$