Surface Area and Volume of Cones Goal: Students will find the surface area and volume of cones.

Lateral Areas and Surface Areas of Cones A cone is like a pyramid, but its base is circular, and the vertex is not in the same plane as the base. The radius of the base is the radius of the cone. The height is the perpendicular distance between the vertex and the center of the base, called the altitude. The slant height, l, is the distance between the vertex and a point on the base edge.

A The lateral surface of a cone consists of all segments that connect the vertex with points on the base edge.

Theorem 12.5 Surface Area of a Right Cone: Lateral Area: LA = πrl Surface Area: S = πrl + B S = πrl + πr2 where B = Area of the Base l = slant height r = radius of cone

Ex. 1: The radius of the base of a cone is 6 m. Its height is 8 m Ex.1: The radius of the base of a cone is 6 m. Its height is 8 m. Find its lateral and surface area to the nearest tenth. Ex.2: The radius of the base of a cone is 15 cm. Its height is 20 cm. Find its surface area to the nearest tenth.

Ex.3: A traffic cone can be approximated by a right cone with radius 5.7 inches and height 18 inches. Find the approximate lateral area and surface area of the traffic cone to the nearest tenth.

Volume of Cones Theorem 12.10 Volume of a Cone: Volume: where h is the height of the cone r is the radius of the cone

Ex.4: Find the volume of the solid.

Ex. 6: Find the volume of the solid. Ex Ex.6: Find the volume of the solid. Ex.7: Find the volume of the solid shown.

Ex.8: Originally, the pyramid had height 144 meters and volume 2, 226, 450 cubic meters. Find the side length of the square base. Ex.9: The volume of a right cone is 1350π cubic meters and the radius is 18 meters. Find the height of the cone.

Ex.10: Find the surface area of the solid. Round to two decimal places.