Question

Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder B?

Answer 1

Answer:

Cylinder B has a volume of 360 cm³

Step-by-step explanation:

The volume of a regular cylinder is: $V = (base)(height)$

The base of a cylinder is a circle with an area πr²

So the volume of a cylinder is: V= πr² (base)

In this case, since we know the two cylinders have the same base and height. Then one can use Cavalieri's Principle which states that  two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal (Kern and Bland 1948, p. 26).

Therefore, it does not matter that the slant lenght differs because the altitude and base remain unchanged.

Answer 2

Check your book on Cavalieri's Principle.

Cavalieri's Principle:

two solids that have the same altitude and identical cross-sections all the way up, though slanted or not, have the same volume.