Fluid force integration problem

[tobywashere]

Homework Statement

The vertical triangular plate shown in the picture below is the end plate of a feeding trough full of hog slop, weighing 80 pounds per cubic foot. What is the force against the plate?

Homework Equations

This question is supposed to involve intregration to find volume.

The Attempt at a Solution

I rotated the triangle around the y-axis (not sure if this is what I'm supposed to do). Then I found the volume of the resulting shape (it is a cone).
V = pi * 4² * 2 / 3
V = 33.5 cubic feet
Then multiply by 80 lbs per cubic foot to get 2680.8 lbs
But this answer is much higher than the textbook's answer. I'm lost for any other way of doing this question. I know my answer can't be right because I didn't integrate anywhere.

 

[mighty2000]

Hello, thank you for sharing your attempt at a solution. You are on the right track by rotating the triangle around the y-axis to create a cone. However, you are missing a key step in the integration process. In order to find the volume of the cone, you need to set up an integral that takes into account the variable radius of the cone as it extends from the base to the top. Remember, the volume of a cone is given by V = (1/3) * pi * r^2 * h, where r is the radius and h is the height. Since the height of the cone is changing as you move up from the base, you need to set up an integral that takes this into account. I would suggest setting up the integral from the base of the cone to the top, with the variable radius as the function to be integrated. Once you have the integral set up correctly, you can then solve for the volume and multiply by the density of the hog slop to find the force against the plate. I hope this helps and good luck with your problem!