Calculus 1- Related Rates Problem(Draining Tank)

Question

Water is draining from a right cylindrical tank at 5 l/s. The tank has a radius of 4 m and is 15 m tall. How fast is the height of the water changing when the height of the water in the tank is 7 m?

Answer 1

Since V = PI*R^2*H for right cylinder simply differentiate both sides with respect to T keeping in mind the chain rule and product rule

dV/dt = Pi*2R*dr/dt*h + pi*R^2&dh/dt

Since the radius is not changing dr/dt = 0 dropping off first term or

dV/dt = pi*R^2*dh/dt

Plug in values dV/dt = 5 (change in volume, R = 4 and solve for dh/dt = 1/(2pi)