9-4Surface Areas of Prisms and Cylinders

Objective – Find the surface area of prisms and cylinders.

CA Geometry Standard 9.0

Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

Types of Prisms

Pentagonal Prism

Triangular Prism

Lateral Faces

Lateral Edges

BasesBases

Oblique Prism

h

Right Prism

h

Formulas You Need to Remember:

Area of a Triangle → A = bh ÷ 2

Area of Parallelogram → A =bh

Area of Trapezoid → A = h(b1 + b2) ÷ 2

Key Concept(s):

Lateral Area and Surface Area of a Prism

phAL ..Lateral Area

Base Perimeter

Height

BALAS 2.... Surface

AreaLateral Area

Area of the

Base(s)

Base Perimeter

h

Base Area

Find the surface area of the regular hexagonal prism.

12 m6 m

PhL )6(6P 36

BALAS 2....

apB2

1

)12(36L2m 432L 30

60m 3

m 33

36332

1B

354B2m 5.93B

2m 432L 2m 5.93B)5.93(2432S

187432 S2m 619S

#1 Finding the Surface Area of a Prism

6

360

2

6030

P = 36

#2 Finding the Surface Area of a Prism

Find the surface area of the triangular prism.

12 cm

5 cm

5 cm 6 cm

BALAS 2....

PhAL .. bhB2

1

)15(2192.. AS2cm 222.. AS

)12(16.. ALP = 162cm 192.. AL

)5)(6(5.0B2cm 15B

Key Concept(s):

Lateral Area and Surface Area of a Cylinder

rhAL 2.. Lateral Area

Radius Height

BALAS 2.... Surface

AreaLateral Area

Base Area

Radius

h

Base Area

2rB

#3 Finding the Surface Area of a Cylinder

10 cm

5 cm

rhAL 2.. BALAS 2....

)10)(5(2.. AL

Find the surface area of a cylinder with height 10 cm and radius 5 cm in terms of pi.

2cm 100.. AL

2rB 2)5(B

2cm 25B)25(2100.. AS 2cm 150.. AS

#4 Finding the Surface Area of a Cylinder

9 ft

6 ftrhAL 2.. BALAS 2....

)9)(6(2.. AL

Find the surface area of a cylinder with radius 6 ft and height 9 ft in terms of pi.

2ft 108.. AL

2rB 2)6(B

2ft 36B)36(2108.. AS 2ft 180.. AS

Example: Find the surface area of a cylinder with

radius 3 ft and height 6 ft. S.A. = 2πrh + 2B

7 ft

5 ft

Example: Find the surface area of the triangular

prism. S.A. = ph + 2B

7 cm

5 cm 4 cm

10 cm

Homework

Pre-AP Textbook pg.491 #1-14 Evens