several hours ago, I saw the problem involving geometry. The problem is tell about truncated cylinder.
I want to know how to derive the formula of volume and its surface area without calculus, but still don't get it.
I've just can found the definition and the volume without proof from:
http://encyclopedia2.thefreedictionary.com/Truncated+Cylinder
Truncated cylinder is the geometric solid produced when a cylinder is cut by a plane that is not parallel to the base.
The volume of a truncated circular cylinder is $V = \frac{\pi r^2(h1 + h2)}{2}$, where $h1$ and $h2$ are the lengths of the longest and shortest elements of the cylinder and $r$ is the radius of the base.
But, there are no proof here, how can I prove this formula? And also is it possible to find the surface area for this kind of the cylinder?
Edit: I've just found the formula of its surface area(without proof too). Here is the link:
http://www.math24.net/cylinder.html
But, how can I got the Area of the bases of a truncated cylinder? In this formula, the root form is appears. How can I got the root form?
Thanks