Thread: volume of oil tanker

Here's a neat integration problem. Not particularly difficult, but cool. Give it a go if you have a mind to.

"The tank of an oil truck is 18 feet long and has elliptical cross-sections that are 6 feet wide and 4 feet high. Find the volume of the oil in the tank in terms of the depth h of the oil".

This one is a little different in that the cross sections are elliptic rather than circular. We have all seen these types of tankers on the road, it got me to thinking about such a problem.

I thought someone would bite on this problem. Here's how I done it. It appears to check. I just made up those dimensions from looking at one of those types of tankers on the road. we could've derived a general case instead.

Since the ellipse is 6 feet wide and 4 feet high, the ellipse has the equation



Solve for x in terms of y:





Now, integrate and we get:



For the general case, from



Kind of long connected and probably simplifies, but that's all I'm doing.

Originally Posted by galactus

Here's a neat integration problem. Not particularly difficult, but cool. Give it a go if you have a mind to.

Originally Posted by galactus

I thought someone would bite on this problem...

I didn't notice it before... Not that I would have been able to do it yet anyway.

Patience Galactus, soon I will be answering all these questions... (This term actually We'll be starting with this kind of work.)