Question

A water tank has the shape of an inverted cone of height 9 m with a circular base of radius 3 m. If water is being pumped into the tank at 4 m/min, how fast is the water level rising when the water is 3 m deep Round your answer to two decimal places The water level is rising at a rate of Number Units

Answer 1

Solution:-

Given that

A water tank has the shape of an inverted cone of height 9 m with a circular base of radius 3m.

if water is being pumped into the tank at 4 $m^3/min$ .

3 deep

3 9

T= -h 3

$h=3r$

when h = 3

$r=\frac{3}{3}$

r = 1

$V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2(3r)$

$V=\f\pi r^3$

$\frac{dV}{dt}=\pi3 r^2\frac{dr}{dt}$

$4=\pi3 r^2\frac{dr}{dt}$

$4=\pi*3 (1)^2\frac{dr}{dt}$

$\frac{4}{3\pi}=\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{4}{3\pi}$

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