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.
• 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. 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:
1 2
Volume: V   r h
3
where h is the height of the cone
r is the radius of the cone
Ex.4: Find the volume of the solid.
Ex.5: Find the volume of the solid.
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.