The radius of spherical balloon is decreasing at the rate of 0.1 cm/sec, the rate at which its volume is decreasing, when its radius is 0.5 cm is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{\pi}{10}cm^3/sec$
$V=\frac{4}{3}\pi r^{3}$
$\frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt}$
$\frac{dr}{dt}=-0.1\,$ cm/s, $r=0.5$ cm
$\frac{dV}{dt}=4\pi(0.5)^{2}(-0.1)$
$=4\pi(0.25)(-0.1)$
$=-0.1\pi$
The volume is decreasing at the rate $0.1\pi\,$ cm$^{3}$/sec.