Name
LESSON
Date
Class
Practice A
10-4 Surface Area of Prisms and Cylinders
Write each formula.
1. lateral area of a right prism with base perimeter P and height h
2. lateral area of a right cylinder with radius r and height h
3. surface area of a right prism with lateral area L and base area B
4. surface area of a cube with edge length s
5. surface area of a right cylinder with radius r and height h
L Ph
L 2rh
S L 2B
S 6s 2
S 2rh 2r 2
Find the lateral area and surface area of each right prism.
6.
M
7.
6 cm
M
M
6 cm
M
4 cm
the rectangular prism
the triangular prism
L 120 cm 2; S 168 cm 2
8. a cube with edge length 2 ft
L 160 m 2; S 280 m 2
L 16 ft 2; S 24 ft 2
Find the lateral area and surface area of each right cylinder.
Give your answers in terms of .
2 in.
9.
10. a cylinder with a radius of 3 mm and a
height of 10 mm
2 in.
L 8 in2; S 16 in2
L 60 mm2; S 78 mm2
A builder drills a hole through a cube of concrete, as
shown in the figure. This cube will be an outlet for a
water tap on the side of a house. Complete Exercises 11–14
to find the surface area of the figure. Round to the nearest
tenth if necessary.
8 in.
1 in.
8 in.
8 in.
2
384 in
2
50.3 in
2
6.3 in
11. Find the surface area of the cube.
12. Find the lateral area of the cylinder.
13. Find twice the base area of the cylinder.
14. The surface area of the figure is the surface area of the prism
plus the lateral area of the cylinder minus twice the base area
of the cylinder. Find the surface area of the figure.
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27
428.0 in2
Holt Geometry
Name
Date
Class
Name
Practice A
LESSON
10-4 Surface Area of Prisms and Cylinders
Date
Practice B
LESSON
10-4 Surface Area of Prisms and Cylinders
Write each formula.
Find the lateral area and surface area of each right prism. Round to the
nearest tenth if necessary.
L � Ph
L � 2�rh
S � L � 2B
S � 6s 2
S � 2�rh � 2�r 2
1. lateral area of a right prism with base perimeter P and height h
2. lateral area of a right cylinder with radius r and height h
3. surface area of a right prism with lateral area L and base area B
4. surface area of a cube with edge length s
5. surface area of a right cylinder with radius r and height h
1.
8. a cube with edge length 2 ft
2
���
2
2
2
2 in.
2
5. a cylinder with base area 169� ft and a
height twice the radius
6. a cylinder with base circumference 8 � m
and a height one-fourth the radius
2
10 cm
6 cm
L � 676� ft 2; S � 1014� ft 2
L � 8� m2; S � 40� m2
Find the surface area of each composite figure. Round to the nearest tenth.
10. a cylinder with a radius of 3 mm and a
height of 10 mm
2 in.
2
L � 60� cm2; S � 110� cm2
4.
Find the lateral area and surface area of each right cylinder.
Give your answers in terms of �.
9.
2
L � 1600 in ; S � 2400 in
Find the lateral area and surface area of each right cylinder.
Give your answers in terms of �.
L � 160 m ; S � 280 m
L � 16 ft ; S � 24 ft
L � 70 mm2; S � 83.8 mm2
2
3. a cube with edge length 20 inches
the triangular prism
2
L � 120 cm ; S � 168 cm
the regular pentagonal prism
L � 176 mi ; S � 416 mi
����
the rectangular prism
2 mm
the rectangular prism
����
���
6 cm
4 cm
7 mm
12 mi
2
7.
6 cm
2.
4 mi
10 mi
Find the lateral area and surface area of each right prism.
6.
Class
7.
����
8.
4 in.
4 in.
3 in.
����
����
A builder drills a hole through a cube of concrete, as
shown in the figure. This cube will be an outlet for a
water tap on the side of a house. Complete Exercises 11–14
to find the surface area of the figure. Round to the nearest
tenth if necessary.
8 in.
1 in.
9.
8 in.
384 in
50.3 in2
2
6.3 in
13. Find twice the base area of the cylinder.
14. The surface area of the figure is the surface area of the prism
plus the lateral area of the cylinder minus twice the base area
of the cylinder. Find the surface area of the figure.
113.7 in2
10.
1 cm
2 ft
1 cm
10 cm
2
11. Find the surface area of the cube.
2 in.
123.7 km2
Describe the effect of each change on the surface area of the given figure.
8 in.
12. Find the lateral area of the cylinder.
5 in.
����
L � 60� mm2; S � 78� mm2
L � 8� in2; S � 16� in2
1 ft
The dimensions are multiplied by 12.
The dimensions are divided by 4.
The surface area is multiplied by 144. The surface area is divided by 16.
Toby has eight cubes with edge length 1 inch. He can stack the cubes into three
different rectangular prisms: 2-by-2-by-2, 8-by-1-by-1, and 2-by-4-by-1. Each prism
has a volume of 8 cubic inches.
2
428.0 in
2-by-2-by-2
8-by-1-by-1
11. Tell which prism has the smallest surface-area-to-volume ratio.
12. Tell which prism has the greatest surface-area-to-volume ratio.
27
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Name
Date
Class
Practice C
LESSON
10-4 Surface Area of Prisms and Cylinders
Holt Geometry
Name
����
5 in.
52 in
Surface Area
The surface area of a right prism with lateral
area L and base area B is
Lateral and Surface Area of a Right Cylinder
30 m
10 m
Lateral Area
The lateral area of a right cylinder with
radius r and height h is
Surface Area
The surface area of a right cylinder with
lateral area L and base area B is
the right triangular prism
L � 2�rh.
2153.1 m2
5.
16 ft
6.
2 yd
lateral
face
S � L � 2B, or S � Ph � 2B.
25 m
2
�
The lateral area of a right cylinder is the curved surface that connects the
two bases. The surface area is the total area of the curved surface and the bases.
35 m
2 in.
the rectangular prism with no top
The lateral area of a right prism with base
perimeter P and height h is
L � Ph.
Find the surface area of each figure. Round to the nearest tenth if necessary.
4.
Lateral Area
������
surface area allows the heat to be radiated into the air more rapidly.
3 in.
Holt Geometry
Lateral and Surface Area of a Right Prism
31,840 mm2
������
Explain why the heat sink has fins. Possible answer:
The fins greatly increase the surface area of the heat sink. The large
3.
Class
The lateral area of a prism is the sum of the areas of all the lateral faces. A lateral
face is not a base. The surface area is the total area of all faces.
����
1. Find the surface area of the heat sink in square millimeters.
2.
Date
Reteach
LESSON
10-4 Surface Area of Prisms and Cylinders
����
A heat sink is a chunk of metal that draws unwanted heat away from
delicate electronic components and releases the heat into the air. The
figure shows a typical heat sink for a desktop computer processor chip.
Each fin is 2 mm wide and is 4 mm from the next fin.
28
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lateral
surface
�
2
S � L � 2B, or S � 2�rh � 2�r .
17 ft
3 yd
Find the lateral area and surface area of each right prism.
the oblique quadrilateral prism with
each edge measuring 3 yards
������
9 ft
6 cm
3 cm
1 cm
������
L � 78 ft ; S � 150 ft
3 cm
3 cm
2
45.7 mm
9. Draw a net of the oblique cylinder in Exercise 6.
����
2
1 cm
������
99.5 cm2
3.
4.
8 cm
6 in.
�����
����
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All rights reserved.
2
L � 86.8 cm ; S � 96.8 cm
5 in.
�����
�����
29
2
2
Find the lateral area and surface area of each right cylinder.
Give your answers in terms of �.
3 cm
������
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All rights reserved.
������
����
4 ft
3 cm
8.
7.
����
3 ft
1156.1 ft 2
48 yd 2
�������
2.
1.
the oblique cylinder
15 cm
2
2
L � 120� cm ; S � 152� cm2
2
L � 60� in ; S � 110� in
�����
Holt Geometry
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All rights reserved.
73
30
Holt Geometry
Holt Geometry