(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A compressible liquid has density which varies with height. AT the level ofhmeters above the bottom, the density is 40(5 -h) kg/m^{3}

a) The liquid is put in the containers below. The cross sections of the container are isosceles triangles. It has straight sides and looks like a triangular prism. How many kg will it hold when placed as shown on the left, resting on one triangular side?

^There is a picture of the object.

2. Relevant equations

Mass = Volume times Density

3. The attempt at a solution

My theory is that since M = V*D, and you're given the density, should I slice and solve for volume, then evaluate the integral of volume and the given integral for density then multiply the results to get the mass?

[tex]\int^{4}_{0}2.5 dh[/tex] and [tex]40\int^{4}_{0}5-h dh[/tex]

I got to the first integral by taking the volume of the first slice (triangular prism):

[tex]\sum\frac{1}{2}b*l*\Delta h[/tex] [tex]\rightarrow[/tex] [tex]\sum\frac{1}{2}2*2.5\Delta h[/tex] [tex]\rightarrow[/tex] lim as [tex]\Delta h[/tex] [tex]\rightharpoonup[/tex][tex]\int^{4}_{0}2.5 dh[/tex]

To find the mass, according to the equation M=VD, should I solve both integrals , one being V and one being D, then multiply?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Density, Volume and Slicing Problem

**Physics Forums | Science Articles, Homework Help, Discussion**