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 . 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 , then the volume of the cylinder is times the volume of the prism. v