Final answer:
Cavalieri's Principle is the concept that solids with the same heights and cross-sectional areas at every level have the same volume. To calculate the volume of a cylinder, you multiply the cross-sectional area by the height.
Step-by-step explanation:
The idea of viewing solids as slices that can be moved around without affecting the volume is called Cavalieri's Principle. This principle implies that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
To find the volume of a cylinder, we use the formula V = A∙h, where V is the volume, A is the area of the base (or cross-section), and h is the height. If we know the radius of a cylinder (r), we can calculate the cross-sectional area as A = πr² (since the base of a cylinder is a circle). Then, by multiplying the area by the height, we get the volume.
Therefore, using Cavalieri's Principle and the formula for the volume of a cylinder, if we know the cross-sectional area A and the difference in height (h2 - h1), the volume of the cylinder can be calculated by multiplying these two values together: V = (h2 - h1)A.