- #1

MANGOMOJO

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## Homework Statement

A horizontal cylindrical drum is 2m in diameter and 4m long. The drum is slowly filled with benzene (density = 0.879g/cm^3). Derive a formula for W, the weight in Newtons of the benzene in the tank, as a function of h, the depth of the liquid in centimeters.

## Homework Equations

We were not given any specific equations, but from attemting to do the solving I use:

Density = m/V

W=ma=mg

V=(pi)r^2h

## The Attempt at a Solution

I have brainstormed. The volume of the drum is 4(pi)=12.56637. I believe that the problem wants for us to use W(h)=?? when finding the equation, and I understand we want to see that as the benzene increases the container becomes heavier. Also, we have the density.

Density = (m/V)

and W=mg, so W=V(density)g

We could plug things in.

W=(0.879)(9.8)V and get W=(8.7906)V

But here is where I am stuck. Does W=(8.7906)V equal W(h)? And should this be a relationship w/time since the benzene is flowing into the drum? I know this could include related rates (calculus) somewhere, but not sure where. Also, where does the drum's volume come in?