7–7 Surface Area of Prisms and Cylinders - Weebly

7?7 Surface Area of Prisms and Cylinders

MAIN IDEA

? Find the lateral and total surface areas of prisms and cylinders.

BUILD YOUR VOCABULARY (pages 167?168)

A lateral face of a solid is any .

surface that is not a

The lateral surface area is the

lateral

.

of the areas of its

The total surface area is the sum of the surfaces.

of all its

KEY CONCEPT

Surface Area of a Rectangular Prism The surface area S of a rectangular prism with length , width w, and height h is the sum of the areas of the faces.

EXAMPLE Surface Area of a Rectangular Prism

Find the lateral and total surface area of the rectangular prism.

7 mm 15 mm

Perimeter of Base P = 2 + 2w

Area of Base B= w

P = 2

+ 2

or

B =

?

or

9 mm

Use this information to find the lateral and total surface area.

Lateral Surface Area L = Ph

Total Surface Area S = L + 2B

L = 48

or

S =

+ 2 ?

or

The lateral surface area is the total surface area is

, and .

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

182 Math Connects, Course 3

7?7

Check Your Progress Find the lateral and total surface area of the rectangular prism.

??V

??V x?V

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

REVIEW IT

What is the formula for finding the area of a triangle? How does this relate to finding the surface area of a triangular prism? (Lesson 7-1)

EXAMPLE Surface Area of a Triangular Prism

CAMPING A family wants to reinforce the fabric of their tent with a waterproofing treatment. Find the total surface area, including the floor, of the tent below.

A triangular prism consists of two

6.3 ft

congruent

faces and

5 ft 5.8 ft

5.8 ft

three

faces.

Draw and label a net of this prism. Find the area of each face.

bottom

?

= 29

left side

?

= 36.54

right side two bases

?

(2 _1 ? 5 ? 2

= 36.54

) = 29

The surface area of the tent is 29 + 36.54 + 36.54 + 29,

or about

.

???v?

x?n?v?

x?n?v? ???v?

x?v?

x?v?

x?n?v?

Math Connects, Course 3 183

7?7

?

ORGANIZE IT

On index cards, write these formulas for finding surface area. Then sketch and label each figure. Place the cards in the "Area" pocket of your Foldable.

?i> 6?i

Check Your Progress Julia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism.

?? {?x?

??x? ??

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

KEY CONCEPT

Surface Area of a Cylinder The surface area S of a cylinder with height h and radius r is the area of the two bases plus the area of the curved surface.

EXAMPLE Surface Area of a Cylinder

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

2 m 5 m

Lateral Surface Area L = 2rh L = 2

Total Surface Area S = L + 2r2

S

+ 2

L =

S

The lateral surface area is about

,

and the total surface area is about

.

HOMEWORK ASSIGNMENT

Page(s): Exercises:

Check Your Progress Find the lateral and total surface area of the cylinder. Round to the nearest tenth.

??

n?

184 Math Connects, Course 3

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