Download Accelerated Geometry Name___________________ 12.3: Surface

Accelerated Geometry
12.3: Surface Areas of Circular Solids
Name___________________
Date_______
Objective: After this lesson, you will be able to find the surface area of cylinders, cones, and
spheres.
CYLINDER
Characteristics:
1. The 2 bases are parallel circles.
2. The altitude of a cylinder is a segment that is
perpendicular to the bases.
3. The axis is a segment which connects the centers
of the circles. In a right cylinder, the axis and the
altitude can be the same segment.
Right
Cylinder
Oblique
Cylinder
Lateral Surface Area:
LSA =
Total Surface Area:
TSA =
Example 1: Find the lateral and total surface area of the right cylinder shown.
12”
r = 2.865 ”
Example 2: Find the height of a right cylinder if the diameter is 10 cm and the TSA = 110π.
Accelerated Geometry
12.3: Surface Areas of Circular Solids
Name___________________
Date_______
CIRCULAR CONE
Characteristics:
1. Resemble pyramids but the base is a circle.
2. The axis is a segment which connects the
center of the circle to the vertex.
3. The altitude of the cone is perpendicular to the
base and connects the vertex to the base.
RIGHT CIRCULAR CONE
Characteristics:
1. All of the characteristics of a circular cone apply.
2. The axis and the altitude are the same segment.
3. The slant height, represented by the letter l, is the distance from the vertex to the
circumference of the base.
Lateral Surface Area:
LSA =
Total Surface Area:
TSA =
Example 1: Find the lateral and total surface area of the right circular cone given.
Example 2: Given the total surface area of a right circular cone is 55π and a slant height of 6,
find the radius.
Accelerated Geometry
12.3: Surface Areas of Circular Solids
Name___________________
Date_______
SPHERES
Characteristics:
1. Definition – a figure in space that is the set of all points that are a given
distance from the center.
2. Great Circle of a sphere – the intersection of a plane and a sphere when
the plane passes through the center of the sphere.
Total Surface Area:
TSA =
Example 1: Find the TSA of the sphere.
12
Example 2: Find the radius of a sphere whose surface area is 300π.
Accelerated Geometry
12.3: Surface Areas of Circular Solids
Name___________________
Date_______
FRUSTUM: the solid below a cross section
l = 13 in, r2 = 15 in, r1 = 10 in.
LSA = __________________
TSA = __________________
Review 1: Find the TSA of the right prism (remember, the faces of a prism are parallelograms)