Complete the derivation of the formula for a cylinder
whose height is equal to its radius.
Suppose the height of a cylinder is equal to its radius.
The cylinder can fit inside a square prism, as shown
below.
The cross-sectional areas are still the same and the ratio
of the area of the circle to the area of the square is still I
The prism's volume is the area of the base,
times the height,
4
Since the ratio of the areas is , then the volume of the
times the volume of the prism.
cylinder is
r
2r
V = (413), or