# Surface Areas of Cylinders Contributed by: In this pdf, we will be learning about the surface area of cylinders. The surface area S of a cylinder is the sum of the areas of the bases and the lateral surface.
1. English Spanish
6.3 Surface Areas of Cylinders
How can you find the surface area of
S
STATE a cylinder?
STANDARDS
MA.7.G.2.1
1 ACTIVITY: Finding Area
Work with a partner. Use a
cardboard cylinder.
● Talk about how you can find the
area of the outside of the roll.
● Use a ruler to estimate the area
of the outside of the roll. Cut
● Cut the roll and press it out flat.
Then find the area of the flat-
tened cardboard. How close is
your estimate to the actual area?
Base
r
Lateral h The surface area of a cylinder is the sum of
surface the areas of the bases and the lateral surface.
Base
2 ACTIVITY: Finding Surface Area
Work with a partner.
● Trace the top and bottom of a can on paper. Cut out the
two shapes.
● Cut out a long paper rectangle. Make the width the same
as the height of the can. Wrap the rectangle around the
can. Cut off the excess paper so the edges just meet.
● Make a net for the can. Name the shapes in the net.
● How are the dimensions of the rectangle related to the
dimensions of the can?
● Explain how to use the net to find the surface area of
the can.
262 Chapter 6 Surface Areas of Solids
2. English Spanish
3 ACTIVITY: Estimation
Work with a partner. From memory, estimate the dimensions of the real-life
item in inches. Then use the dimensions to estimate the surface area of the
item in square inches.
a. b. c.
d.
4. IN YOUR OWN WORDS How can you find the surface area of a cylinder?
Give an example with your description. Include a drawing of the cylinder.
5. To eight decimal places, π ≈ 3.14159265. Which of the following is
closest to π ?
22 355
a. 3.14 b. — c. —
7 113
“To approximate the irrational “Then I compute the rational
number Ƽ 3.141593, I simply number Ƽ 3.141593.”
remember 1, 1, 3, 3, 5, 5.”
Use what you learned about the surface area of a cylinder to
complete Exercises 5 – 7 on page 266.
Section 6.3 Surface Areas of Cylinders 263
3. English Spanish
6.3 Lesson
Lesson Tutorials
Area, A = π r 2 Circumference, C = 2π r
The diagram reviews some
important facts for circles. Radius, r
Surface Area of a Cylinder
Words The surface area S of a cylinder is the sum of the areas of the
bases and the lateral surface. Base
Remember r r
2π r
circumference
π = —— h
diameter
Pi can be approximated Lateral surface h
22
as 3.14 or —.
7 Algebra S = 2π r 2 + 2π rh
r
Area of Area of Base
bases lateral surface
EXAMPLE 1 Finding the Surface Area of a Cylinder
Find the surface area of the cylinder. Round your answer to the
4 mm
nearest tenth.
3 mm Draw a net.
4 mm
S = 2π r 2 + 2π rh
= 2π (4)2 + 2π (4)(3)
= 32π + 24π 3 mm
= 56π ≈ 175.8
The surface area is about 4 mm
175.8 square millimeters.
1. A cylinder has a radius of 2 meters and a height of 5 meters.
Exercises 8 –10 Find the surface area of the cylinder. Round your answer to
the nearest tenth.
264 Chapter 6 Surface Areas of Solids
4. English Spanish
EXAMPLE 2 Finding Surface Area
How much paper is used for the label on 1 in.
the can of peas?
Find the lateral surface area of the cylinder.
2 in.
Do not include the area of
S = 2π rh the bases in the formula.
= 2π (1)(2) Substitute.
= 4 π ≈ 12.56 Multiply.
About 12.56 square inches of paper is used for the label.
EXAMPLE 3 Real-Life Application
You earn \$0.01 for recycling the can in Example 2. How much can you
2 in. expect to earn for recycling the tomato can? Assume that the recycle
value is proportional to the surface area.
Find the surface area of each can.
Tomatoes Peas
S = 2π r + 2π rh
2
S = 2π r 2 + 2π rh
5.5 in.
= 2π (2)2 + 2π (2)(5.5) = 2π (1)2 + 2π (1)(2)
= 8 π + 22π = 2π + 4 π
= 30π = 6π
Use a proportion to find the recycle value x of the tomato can.
surface area
30 π in.2 6π in.2
—=—
x \$0.01 recycle value
⋅ ⋅
30π 0.01 = x 6 π Use Cross Products Property.
5 ⋅ 0.01 = x Divide each side by 6π.
0.05 = x Simplify.
You can expect to earn \$0.05 for recycling the tomato can.
2. WHAT IF? In Example 3, the height of the can of peas
Exercises 11–13 is doubled.
a. Does the amount of paper used in the label double?
b. Does the recycle value double? Explain.
Section 6.3 Surface Areas of Cylinders 265
5. English Spanish
6.3 Exercises
Help with Homework
1. CRITICAL THINKING Which part of the formula S = 2π r 2 + 2π r h represents
the lateral surface area of a cylinder?
2. CRITICAL THINKING Given the height and the circumference of the base
of a cylinder, describe how to find the surface area of the entire cylinder.
Find the indicated area of the cylinder. 6 cm
3. Area of a base 3 cm
4. Surface area
6)=3
9+(- 3)=
3+(- 9)=
4+(- =
1)
9+(-
Make a net for the cylinder. Then find the surface area of the cylinder. Round your
5. 6. 4m 7.
3 ft 7 ft
2 ft 1m 5 ft
Find the surface area of the cylinder. Round your answer to the nearest tenth.
1 8. 5 mm 9. 6 ft 10.
12 cm
2 mm 6 cm
7 ft
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
2 11. 12. 9 in. 13. 14 m
10 ft
2m
6 ft 4 in.
50 ft
14. TANKER The truck’s tank
is a stainless steel cylinder.
Find the surface area of
the tank.
266 Chapter 6 Surface Areas of Solids
6. English Spanish

15. ERROR ANALYSIS Describe and 6 ft
correct the error in finding the S = 2𝛑 rh
surface area of the cylinder. ≈ 2𝛑 (6)(11)
11 ft
= 132𝛑 ft2
16 in.
16. OTTOMAN What percent of the surface area of the
ottoman is green (not including the bottom)?
6 in.
8 in. 17. REASONING You make two cylinders using 8.5-inch by 11-inch
pieces of paper. One has a height of 8.5 inches and the other
has a height of 11 inches. Without calculating, compare the
surface areas of the cylinders.
18. INSTRUMENT A ganza is a percussion
instrument used in samba music.
a. Find the surface area of each of the two
labeled ganzas.
b. The weight of the smaller ganza is 1.1 pounds.
Assume that the surface area is proportional to
the weight. What is the weight of the larger ganza?
19. BRIE CHEESE The cut wedge represents one-eighth
of the cheese.
cm cm a. Find the surface area of the
5
10 2 4.
cheese before it is cut.
3 in.
3.5 cm b. Find the surface area of
5.5 cm the remaining cheese after
the wedge is removed. Did
the surface area increase,
decrease, or remain the same?
1 in.
20. The lateral surface area of a cylinder is
184 square centimeters. The radius is 9 centimeters. What is the