Question

Find the volume of the cylinder in terms of pi. (h = 6 and r = 3)

Thank you!

Answer 1

the cylinder is not a right-circular cylinder, is rather a slanted cylinder, however, recall Cavalieri's Principle, if the cross-sections of the slanted cylinder are the same as the cross-sections of a right-cylinder at each height, then their volume is the same.

so the volume of this slanted cylinder is really the same volume as a right-circular one,


`\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=6 \end{cases}\implies V=\pi (3)^2(6)\implies V=54\pi`