A water tank, having the shape of a rectangular prism of base 100 square cm, is being filled at the rate of 1L per minute.

Question

What is the rate at which the height of the water in the tank increases? Answer is to be expressed in cm per minutethe conversion is 1 liter =1,000 cm^3

Answer 1

Let V = volume of water at time t

       h = depth of water at time t

 

Given:  dV/dt = 1 L/min = 1000 cm³/min

Find:     dh/dt

 

Solution:  The volume of water at time t is

                 V = (area of base)(height)

 

                 V = 100h

 

                Differentiate with respect to t to get dV/dt = 100(dh/dt)

 

                So, dh/dt = (1/100)(dV/dt)

 

                                  = (1/100)(1000) = 10 cm/min