• Support PF! Buy your school textbooks, materials and every day products Here!

Density, Volume and Slicing Problem

  • Thread starter Eonfluxx
  • Start date
  • #1
5
0

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?
[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?
 

Answers and Replies

  • #2
5
0
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!
 
  • #3
cronxeh
Gold Member
961
10
Last edited by a moderator:

Related Threads on Density, Volume and Slicing Problem

  • Last Post
Replies
3
Views
2K
Replies
7
Views
3K
  • Last Post
Replies
15
Views
2K
Replies
4
Views
2K
Replies
2
Views
991
  • Last Post
Replies
1
Views
9K
Replies
6
Views
6K
Replies
3
Views
8K
Replies
2
Views
2K
Replies
6
Views
352
Top