A right cylinder has height h and radius r. It is sliced by a plane that is tangent to one circular base at A and intersects the other at diameter BC. What is the volume of slice ABCD?
Note that BO=CO=DO=r, AD=h, BC is perpendicular to DO, and AD is perpendicular to DO.
h
-- r -- sqrt(r^2 - x^2) -- - y
| | | r
| | |
Slice Volume = 2 | | | dz dy dx
| | |
| | |
-- 0 -- 0 -- 0
-- r -- sqrt(r^2 - x^2)
| |
h | |
= - | | 2y dy dx
r | |
| |
-- 0 -- 0
-- r
|
h |
= - | (r^2 - x^2) dx
r |
|
-- 0
2
= - h r^2
3
|
|
Posted by Bractals
on 2005-11-25 11:02:15 |
Solution
