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A cylindrical tank with radius 3m is being filled with water at a rate 4m^³/min.How fast is the height of the water increasin?

Sagot :

Given :

A cylindrical tank with radius 3m is being filled with water at a rate 4m³/min.

To Find :

How fast is the height of the water increasing.

Solution :

We know, volume of cylinder is given by :

[tex]V = \pi r^2h[/tex]       ....1)

Also, we have given that, [tex]\dfrac{dV}{dt} = 4 \ m^3/min[/tex] .

Differentiating equation 1) w.r.t  t we get :

[tex]\dfrac{dV}{dt} =3^2 \pi \dfrac{ dh }{dt}\\\\\dfrac{dh}{dt} = \dfrac{4}{3^2 \times \pi}\\\\\dfrac{dh}{dt} = 0.141 \ m/min[/tex]

Therefore, the height of water is increasing at a rate of 0.141 m/min.

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