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 int
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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

\frac{r}{h}=\frac{3}{9}

r=\frac{1}{3}h

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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