Question

Use Cavalieri's Principle to calculate the exact volume of an oblique cylinder with a height of 20 centimeters and a circular base with a radius of 10 centimeters.

Answer 1

the volume of an oblique cylinder is V=2,000\pi\ cm^{3}

Answer 2

The exact volume of an oblique cylinder is
`V=2,000\pi\ cm^(3)`

Explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume

so

The volume of the oblique cylinder is equal to

`V=\pi r^(2) h`

we have

`h=20\ cm`

`r=10\ cm`

substitute

`V=\pi (10)^(2) (20)`

`V=2,000\pi\ cm^(3)`