Surface Area and Volume

The surface area of a pyramid is the lateral area (1/2 x perimeter x slant height) plus the area of the base. The surface area of a prism is 2(lw+wh+lh). The surface area of a cylinder is 2 x pi x radius squared + 2 x pi x radius x height. The surface area of a cone is lateral area (pi x radius x slant height) + area of base.
The volume of a pyramid is 1/3 x lwh because it is one third the volume of a prism, which is lwh. The volume of a cone 1/3 x pi x radius squared x height because it is one third the volume of a cylinder, which is pi x radius squared x height.