Deriving a Formula for Volume of a Cylinder
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
The prism's volume is the area of the base,
times the height,
Since the ratio of the areas is then the volume of the
cylinder is my times the volume of the prism.
V = + (4r3), or