Calc II question:
Given is a picture of a shed that is a half cylinder with radius as "r" and length as "l."
What is the volume of the shed? I found to be (pi*r^2*l)/2
The shed is ﬁlled with sawdust whose density (mass/unit volume) at any point is proportional to the distance of that point from the ﬂoor. The constant of proportionality is k. Calculate the total mass of sawdust in the shed.

Question

Calc II question:
Given is a picture of a shed that is a half cylinder with radius as "r" and length as "l."
What is the volume of the shed? I found to be (pi*r^2*l)/2
The shed is ﬁlled with sawdust whose density (mass/unit volume) at any point is proportional to the distance of that point from the ﬂoor. The constant of proportionality is k. Calculate the total mass of sawdust in the shed.

irishboy123 · Answer

guessing without a drawing, think you're looking at $M = \iiint \rho \ dV = \iiint \ (kr sin \theta) \ r \ dr \ \ d \theta \ dz$ http://www.wolframalpha.com/input/?i=%5Cint_%7Bz%3D0%7D%5E%7BL%7D+%5Cint_%7B%5Ctheta+%3D+0%7D%5E%7B%5Cpi%7D+%5Cint_%7Br+%3D+0%7D%5E%7BR%7D+k+r+sin+%5Ctheta+r+dr+d%5Ctheta+dz

irishboy123 · Answer

i am travelling today so might be of limited use to you if you are pushing ahead; but there should be loads of clues in there, especially in the integral formed in wolfram; and @Phi is "the" go-to for this kind of stuff.