Question

The right cylinder in the diagram has a volume of 450 cm3. The other cylinder has a slant length of 10 cm, but the same base area and vertical height. What is the volume of the tilted cylinder?

Answer 1

A tilted or slanted cylinder has the same volume as its equivalent right cylinder, provided that
(a) the two bases of the tilted cylinder are parallel,
(b)  the base areas of the tilted and right cylinders are equal,
(c) the vertical height of the right and tilted cylinders are equal.

This fact can be verified by slicing the tilted cylinder into thin, flat washers, as in integral calculus.

Because all 3 conditions are satisfied, the volume of the tilted cylinder is 450 cm³.

Answer: 430 cm³