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.

Respuesta :

Answer:

The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]

Step-by-step 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

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=20\ cm[/tex]

[tex]r=10\ cm[/tex]

substitute

[tex]V=\pi (10)^{2} (20)[/tex]

[tex]V=2,000\pi\ cm^{3}[/tex]

Answer:

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