Question

Need some help with this. Its been a long time since I did these. A container is formed by rotating the graph of y = 1/x about the y axis in the interval y=1 and y=h. Water is poured into the vessel at the rate of 1.5 m^3 per minute. Calculate the rate of increase of level of the water when its height is 2 m.

Answer 1

Volume of the vessel is pi * INTegral of 1/y^2 in the interval 1 to h. Right?

Answer 2

This is a problem about related rates which I only vaguely remember!

Answer 3

Simplifying, volume of rev about the y-axis to get \(V(y)\), and then chain rule: \(\frac {dV}{d t} = \frac{dV}{dy} \frac{dy}{dt}\)

so:

\(\frac{dy}{dt} =\dfrac{ \frac{dV}{dt} }{\frac {dV}{dy}}\)