Surface Area and Volume

A cone has a circular base

A cone has a circular base with center O, vertex A, perpendicular height h, base radius r, and slant height l. The fundamental relationship is l² = h²

A cone has two surfaces

A cone has two surfaces: circular base (area = πr²) and curved surface. The curved surface area = πrl, where l is slant height. Total surface area = π

Volume of cone = (1/3) ×

Volume of cone = (1/3) × πr²h. This is exactly one-third the volume of a cylinder with the same base radius and height. This relationship can be demon

Surface area of sphere = 4πr²

Surface area of sphere = 4πr². For a hemisphere: curved surface area = 2πr², total surface area = 3πr² (includes the flat circular base). This can be

Volume of sphere = (4/3)πr³

Volume of sphere = (4/3)πr³. Volume of hemisphere = (2/3)πr³. The relationship shows that a hemisphere holds exactly twice the volume of a cone with t