Question

An inverted conical container , $R=4cm$ , $H=20cm$ , is full of water . Due to a small leak at the vertex , the volume of the water in the container reduce at $12c{m}^3/sec$. Find the rate at which water level falls when water level is $5cm$ .

Answer 1

REFR.IMage

$R=4cm,H=20cm$.

volume $=\frac{1}{3}\pi r^{2}H$

$=\frac{1}{3}\times \frac{22}{7}\times 4^2\times 20$

volume $=47.87c{m}^3$

(a) $5cm$ height

Volume $=\frac{1}{3}\times \frac{22}{7}{x}^2\times 5$ $\frac{20}{4}=\frac{5}{x}$

$=0.7479c{m}^3$

volume difference $=47.122c{m}^3$

$time=\frac{47.122}{12}=3.9268sec$