Question

A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two

cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.

Answer 1

A. The volumes are the same, based on Cavalieri's principle.

Explanation:

Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.

Application

A right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.