Section 10 – 3

Surface Area Of Prisms & Cylinders

Objective:To find the surface area of a prism

To find the surface area of a cylinder

Base:A polyhedron with exactly two congruent, parallel faces

Prism:

Congruent, parallel faces

Lateral Faces:Faces that ARE NOT bases

We Name a Prism by the Shape of its Bases

Height of Prism:The length of the altitude that joins the two bases

Lateral Area:The sum of the areas of the lateral faces

Surface Area:The sum of the lateral area and the area of the two bases

Example 1 Finding Surface Area of a Prism

A) Use a net to find the lateral and surface area of the rectangular prism below.

B) Use a net to find the lateral and surface area of the triangular prism below.

C) Use a net to find the lateral and surface area of the cube below.

Theorem 10 – 1 Lateral & Surface Area of Prisms

L.A. = ph

S.A. = L.A. + 2B

Example 2 Using Formulas to Find Surface AreaA) Use formulas to find the lateral area and

surface area of the prism.

B) Use formulas to find the lateral area and surface area of the prism.

C) Find the surface area of a 10 cm high prism with triangular bases having 18 cm edges. Round to the nearest whole number.

HOMEWORK

Textbook Page 531 – 532; #1 – 7 All

Section 10 – 3

Continued…Objective:

To find the surface area of a cylinder

Base:

Has two congruent, parallel circle bases

Cylinder:

Congruent, parallel circle faces

Height of Cylinder:The length of the altitude that joins the two bases

Lateral Area:The curved surface between the two bases (when unrolled – it is a rectangle)

Surface Area:The sum of the lateral area and the area of the two bases

Theorem 10 – 2Lateral & Surface Area of Cylinders

L.A. = ch Or 2πrh

S.A. = L.A. + 2BOr 2πrh +2π

Example 3 Finding Surface Area of a

CylinderA) The radius of the base of a cylinder is 4 in. and its height is 6 in. Find the lateral and surface area of the cylinder in terms of π.

B) Find the lateral and surface area of a cylinder with height 10 cm and radius 10 cm in terms of π.

C) The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its lateral and surface area in terms of π.

Example 4 Real-World Connection

A) The drums of the roller below are cylinders of length 3.5 ft. The diameter of the drum is 4.2 ft. What area does the large drum cover in one full turn? Round your answers to the nearest square foot.

B) A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6 in. high cornmeal container is 4 in. The diameter of the base of the 4 in. high barley container is 6 in. Which container has the greater surface area?

10 – 3 Ditto; #1 – 15 Odd