Answer
a) ${\frac{dV}{dt}}={\frac{1}{3}\pi r^2 \frac{dh}{dt}}$
b) ${\frac{dV}{dt}}={\frac{2}{3}\pi r h \frac{dr}{dt}}$
c) ${\frac{dV}{dt}}={\frac{1}{3}\pi r^2 \frac{dh}{dt}}+{\frac{2}{3}\pi r h \frac{dr}{dt}}$
Work Step by Step
The volume of a hemisphere is (V) =${\frac{1}{3}\pi r^2 h}$
a) Derive when radius is constant and height is changing
${\frac{dV}{dt}}={\frac{1}{3}\pi r^2 \frac{dh}{dt}}$
b) Derive when height is constant and radius is changing
${\frac{dV}{dt}}={\frac{2}{3}\pi r h \frac{dr}{dt}}$
c)) Derive when radius is changing and height is changing
${\frac{dV}{dt}}={\frac{1}{3}\pi r^2 \frac{dh}{dt}}+{\frac{2}{3}\pi r h \frac{dr}{dt}}$
