Atank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measurement in feet). if the tank is full of a fluid weighing 100 pounds per cubic foot, set up an integral for the work required to pump the contents of the tank to a level 5 feet above the top of the tank.

ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving about y axis in the interval .

Density of the fluid in the tank,

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is,

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in in the parabolic equation . This gives,

So, the height of top of tank is,

Now, 5 ft above 'H' means

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

ft

Now, area of cross section of the tank is given as:

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have,

So,

Therefore, radius,

Now, area of cross section is,

Work done in pumping the contents to 5 feet above is given as:

Plug in all the values. This gives,

i hope this is what you were looking for.

see attached graph