Englis yB 2019-2020
Deriving a Formula for Volume of a Cylinder
Suppose the height of a cylinder is equal to its radius. Complete the derivation of the formula for a cylinder
The cylinder can fit inside a square prism, as shown whose height is equal to its radius.
below.
The cross-sectional areas are still the same and the ratio The prism's volume is the area of the base,
of the area of the circle to the area of the square is still
times the height,
.
Since the ratio of the areas is then the volume of
the cylinder is times the volume of the prism.
T
V = (413), or
r
2r