Surface Area of Cones and
Spheres
Cone – The circular
counterpart of a
pyramid. Every cone
has one face that is its
base. This base is a
circular region and lies
in a plane. The point
not in the plane of the
base is called the
vertex of the cone.
Surface Area of Cones and
Spheres
Altitude – The perpendicular line
segment connecting the apex of
the cone to the plane of its base.
The length of this segment is
frequently termed the height of
the cone.
Axis – The segment connecting the
center of one base to the apex.
If the axis is perpendicular to
the plane of the base, the cone
is right. If the axis is not
perpendicular, the cone is
oblique.
Surface Area of Cones and
Spheres
Lateral Area of a Cone
• If a right circular cone
has a lateral area of L
square units, a slant
height of l units, and
the radius of base is r
units, then
L = *r*l
Surface Area of Cones and
Spheres
Surface Area of a Cone
• If a right circular cone
has a surface area of T
square units, a slant
height of l units, and
the radius of the base
is r units, then
T = *r*l + *r2
A hat for a child’s birthday party has a conical shape
with an altitude of 9 inches and a diameter of 5
inches. Find the lateral area of the birthday hat.
Answer: 73.4 in2
Find the surface area of the cone. Round to the
nearest tenth.
Answer: about 63.6 cm2
Surface Area of Cones and
Spheres
Great Circle – When a
plane intersects a
sphere so that the
intersection contains
the center of the
sphere. The radius of
the sphere and the
great circle are the
same length.
Surface Area of Cones and
Spheres
Hemisphere – Half of a
sphere. A great circle
splits a sphere into two
congruent
hemispheres.
In the figure, O is the center of the sphere, and plane
U intersects the sphere in circle L. If OL 3 inches and
LM 8 inches, find OM.
Answer: about 8.5 in.
Surface Area of Cones and
Spheres
Surface Area of a
Sphere
• If a sphere has a
surface area of T
square units and a
radius of r units, then
T = 4**r2
a. Find the surface area of the sphere, given a great circle
with an area of approximately 91.6 square centimeters.
Answer: about 366.4 cm2
b. Find the surface area of a hemisphere with a radius of
6.4 inches.
Answer: about 386.0 in2
Find the surface area of a ball with a circumference of
18 inches to determine how much leather is needed to
make the ball.
Answer: about 103.1 in2