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 StartFraction pi Over 4 EndFraction. StartFraction pi Over 4 EndFraction Complete the derivation of the formula for a cylinder whose height is equal to its radius. The prism’s volume is the area of the base, , times the height, . Since the ratio of the areas is StartFraction pi Over 4 EndFraction, then the volume of the cylinder is times the volume of the prism. V = A cylinder inside of a square prism is shown. The cylinder has a height and radius with a length of r. The length of the square prism is 2 r.(4r3), or
