Two measurements of a cylinder are varying in such a way that the volume is kept constant. If the rates of change of the radius (r) and height (h) are equal in magnitude but opposite in sign, then
Answer & explanation
Correct answer: option 1
Let V be the volume of the cylinder at any time t. Then,
$V=\pi r^2 h$
$\Rightarrow \frac{d V}{d t}=\pi\left\{2 r h \frac{d r}{d t}+r^2 \frac{d h}{d t}\right\}$
$\Rightarrow 0=\pi\left\{2 r h \frac{d r}{d t}-r^2 \frac{d r}{d t}\right\}$ [∵ V = constant and $\frac{d r}{d t}=-\frac{d h}{d t}$]
$\Rightarrow r=2 h$