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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/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.

## 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?

[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?