A large cylinrical tankor radius 40cm contins a liquid and at time,t the depth is h cm. There is a hole in the bottom and liuid leaks out at a rate of 32pi h to power of 0.5. Show at time t, the heighth of the liquid in the tank satisfies the diff. eqn..dh by dt=-0.02 h to power of 0.5.

Question

A large cylinrical tankor radius 40cm contins a liquid and at time,t the depth is h cm. There is a hole in the bottom and liuid leaks out at a rate of 32pi h to power of 0.5. Show at time t, the heighth of the liquid in the tank satisfies the diff. eqn..dh by dt=-0.02 h to power of 0.5.

Thanks

Answer 1

Cross sectional area

=π(40²)
=1600π

change in height per unit time
=dh/dt
=(rate change in volume/cross sectional area)
=-32πh^(0.5)/1600π
=-0.02h^(0.5)

The sign is negative because h decreases with time.