Force alongside the inside of a hemispherical bowl

[DevinTyler]

Homework Statement

There is a bowl filled with milk with a diameter of 16cm. (The density of milk is 1050 kg/m³). Find the total force alongside the inside of the bowl.

Homework Equations

The Attempt at a Solution

I decided to break this problem up. First of all, its the first time we've dealt with a hemisphere, so I wasn't too sure on how to approach it, but this is what I came up with:

Force on the bottom of the bowl (a constant): Bottom: Density * Gravitational Constant * Volume = 1050*9.8*pi*8².

Now, to find the force on the sides using integration. I decided to take a look at the bowl from a top down perspective, doing so, I get a circle. Now, I can apply integrals to calculate every 'ring' from the inside to the outside of the bowl.

(integral from 0 to 8)
$$\int$$2*pi*h * sqrt(64-h²) * 1050 *9.8 dh

I am very unsure if this method would work, but logically...it seems alright with me!

 

[3029298]

I had a quick look and I would do exactly the same thing

 

[DevinTyler]

I had a quick look and I would do exactly the same thing

Thanks, are you sure that the force on the bottom is the right constant? going to the help center, someone said there wouldn't be any force, I just couldn't believe him.