Water is run at a constant rate of ft^3/min to fill a cylindrical tank of radius ft and height ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by integrating. [Take the weight density of water to be lb/ft^3.] Carry out all calculations exactly then round the final answer to one decimal place.

Step-by-step explanation:

Given [Missing from the question]

The volume (V) of a cylindrical tank is:

This gives:

If the rate is given as:

Then the time to fill the tank is:

The weight of the water when the tank is filled up is:

The conjecture about the average weight is:

To check by integrating:

After time t:

The volume (V) of the water in tank is

i.e. from time = 0 to 141.39 minutes

Integrate:

Divide by t

Average Volume =

The calculated value of average volume in both cases is:

a - base

b - exponent

so,