A cylindrical container of height 1 m and diameter 0.5 m is partially filled with maple syrup. When the container is lying on its side, the syrup level at the deepest point is 37.5 cm (three eighths of a meter). What is the liquid level after the container is raised up?

Question

wolf1728 · Answer

The volume formula for a horizontal cylinder is pretty complex. So I used the calculator here: http://www.1728.org/cyltank.htm When a 50 cm diameter horizontal cylinder is filled to the 37.5 cm level, it is 80.45% filled. Therefore, when it is turned vertically, the mathematics work in a linear manner. So, 80.45% full would mean the liquid level is .8045 meters. (Think I might put the formula on that calculator page).

anonymous · Answer

Thanks wolf! I'll try to find the answer. In the meantime, anyone can help w/ the integrals? :S

wolf1728 · Answer

Can't help you with the integrals but I am working on posting the formula for the horizontal cylindrical tank.  (It will probably be ready in a few hours.  I like to make really sure it will be error free.)

wolf1728 · Answer

Hey, I finally wrote the page with the horizontal cylinder formula. (It's more than a formula but anyway it is here: http://www.1728.org/cyltank2.htm