NAME ________________________________________ DATE ______________ PERIOD _____
7-7
Study Guide and Intervention
Surface Area of Prisms and Cylinders
The lateral area of a prism is the perimeter P of the base times the height h of the prism, or Ph.
The total surface area S of a prism is the lateral surface area plus the area of the two bases 2B, or
S 2B or S Ph 2B.
Find the lateral and total surface areas of the rectangular prism.
Perimeter of Base
Area of Base
P 2 2w
B w
P 2(5) 2(3)
B 5(3)
P 16
B 15
7 ft
3 ft
Use this information to find the lateral and total surface areas.
5 ft
Lateral Surface Area Total Surface Area
L Ph
S L 2B
L 16(7) or 112
S 112 2(15) or 142
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
The lateral surface area is 112 square feet and the total surface area of the prism is
142 square feet.
The lateral area L of a cylinder with height h and radius r is the circumference of the base times the
height, or 2rh. The surface area S of a cylinder with height h and radius r is the lateral area
plus the area of the two bases, or S 2r 2 or S 2rh 2r 2.
Example 2
Find the surface area of the cylinder.
Round to the nearest tenth.
Lateral Surface Area Total Surface Area
9m
L 2rh
S L 2r2
L 2 · 3.14(5)(9)
S 282.6 2 · 3.14(5)2
L 282.6
S 439.6
5m
The lateral area is about 282.6 square meters, and the surface area of the
cylinder is about 439.6 square meters.
Exercises
Find the lateral and total surface areas of each solid.
Round to the nearest tenth if necessary.
1.
2.
3.
5 yd
5 cm
8 in.
3 cm
4 in.
2 yd
7 in.
4 yd
Chapter 7
47
Course 3
Lesson 7-7
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
7-7
Skills Practice
Surface Area of Prisms and Cylinders
Find the lateral and total surface areas of each solid. Use 3.14 for .
Round to the nearest tenth if necessary.
1.
2.
3.
5 mm
3 in.
6 ft
3 mm
7 mm
6 in.
4 ft
4 mm
2 ft
4.
5.
6.1 cm
5 cm
6.
6.1 cm
7 yd
10 m
17 cm
7 cm
8m
8 yd
4m
8.
12 mi
9.
11 km
5 mi
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7.
10.4 ft
5 mi
13 mi
6 km
9 ft
5.7 km
10.
11.
12.
15 cm
13 m
18 in.
3
11 5 in.
9 cm
1
7 2 cm
7m
9.4 m
12 cm
13. cube: edge length, 11 m
14. rectangular prism: length, 9 cm; width, 13 cm; height, 18.4 cm
15. cylinder: radius, 9.4 mm; height, 15 mm
16. cylinder: diameter, 28 in.; height, 12.6 in.
Chapter 7
48
Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
7-7
Practice
Surface Area of Prisms and Cylinders
Find the lateral and total surface areas of each solid. Use 3.14 for .
Round to the nearest tenth if necessary.
1.
1 in.
4 in.
2.
1.3 mm
3.
5 ft
1.6 mm
0.8 mm
7 ft
1.1 mm
5 in.
Lesson 7-7
2.1 mm
4 yd
4.
13 cm
5.
7 yd
6.
3m
9 cm
5 yd
2m
2 12 m
5 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8 yd
7. ALGEBRA A rectangular prism has height 4 millimeters and width 5 millimeters. If the
total surface area is 166 square millimeters, what is the length of the prism?
8. WATER A cylindrical-shaped water storage tank with diameter 60 feet and height 20
feet needs to be painted on the outside. If the tank is on the ground, find the surface
area that needs painting.
9. CONCRETE Find the total surface area of the hollow concrete casing shown, including
the interior.
4 in.
8 in.
8 in.
12 in.
Chapter 7
49
Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
7-7
Word Problem Practice
Surface Area of Prisms and Cylinders
1. BAKING The top and sides of the cake
shown below are to be covered in
frosting. Calculate the area that will be
covered with frosting.
2. GIFTS A birthday gift is placed inside
the box shown below. What is the
minimum amount of wrapping paper
needed to wrap this gift?
2 in.
7 in.
9 in.
14 in.
12 in.
10 in.
3. FARMING Phil is planning to shingle
the roof on his barn shown below. How
many square feet will he be shingling?
4. FARMING Refer to Exercise 3. If one
package of shingles covers 325 square
feet, how many packages will Phil need
to buy?
24 ft
27 ft
12 ft
41.6 ft
5. LIGHT SHOW A mirrored cylinder used
in a light show is shown below. Only
the curved side of the cylinder is
covered with mirrors. Find the area of
the cylinder covered in mirrors. Round
to the nearest tenth.
6. SOUP Emily has the flu, so she decides
to make chicken noodle soup. How
many square inches of metal were used
to make Emily’s can of soup? Round to
the nearest tenth.
3 in.
22 cm
1
4 2 in.
30 cm
Chapter 7
50
Course 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
24 ft
NAME ________________________________________ DATE ______________ PERIOD _____
7-7
Enrichment
Sliced Solids
In the diagrams on this page, a plane slices through a solid figure.
The intersection of the plane with the solid is called a cross section.
The drawings for each problem show a sliced solid and the dimensions
of the resulting cross section.
1. One-fourth of the cube is sliced off
the top.
2. One-third of the prism is sliced off
the back.
8 in.
7 in.
8 in.
5 in.
9 in.
4. The cylinder is sliced in half.
16 m
10 cm
14.1 cm
20 m
5. The cylinder is sliced in half.
6. The prism is sliced in half.
56.6 ft
80 m
40 ft
100 ft
100 m
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. The cube is sliced in half.
Chapter 7
51
40 ft
Course 3
Lesson 7-7
Find the surface areas of the two solids that result from the slice.
Use 3.14 for . Round to the nearest tenth.