Density, Volume and Slicing Problem

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Homework Statement


A compressible liquid has density which varies with height. AT the level of h meters above the bottom, the density is 40(5 - h) kg/m3
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?​
DensityPRoblem.jpg

^There is a picture of the object.

Homework Equations


Mass = Volume times Density



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?
\int^{4}_{0}2.5 dh and 40\int^{4}_{0}5-h dh

I got to the first integral by taking the volume of the first slice (triangular prism):
\sum\frac{1}{2}b*l*\Delta h \rightarrow \sum\frac{1}{2}2*2.5\Delta h \rightarrow lim as \Delta h \rightharpoonup\int^{4}_{0}2.5 dh

To find the mass, according to the equation M=VD, should I solve both integrals , one being V and one being D, then multiply?
 
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Ah... It's starting to make more sense now, thanks. So since density is varying with the height we make it all one integral rather than separate ones. Part B is the same question except with the 4m on the ground on its point with the rectangle side up. I figured once I'd managed A, B would be simple. Thanks!
 
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