Chapter 12.4 Surface Area of Cylinders

1
Chapter 12.4Surface Area of Cylinders
2
Objectives

• Find lateral areas of cylinders
• Find surface areas of cylinders

3
The axis of the cylinder is the segment with
endpoints that are centers of the circular bases.
If the axis is also the altitude, then the
cylinder is called a right cylinder. Otherwise,
the cylinder is an oblique cylinder.
Base
Right Cylinder
Base
Oblique Cylinder
Axis
Axis
Altitude
Altitude
Base
Base
4

• A cylinder is composed of two congruent circles
  and a rectangle. The area of this rectangle is
  the lateral area. The length of the rectangle is
  the same as the circumference of the base, 2pr.
  So, the lateral area of a right cylinder is 2prh

h
2 r
5
If a right cylinder has a lateral area of L
square units, a height of h units, and the bases
have radii of r units, then L 2prh.
Lateral Area of a Cylinder
2pr
h
6

• Sawyer needs to find out the lateral area for his
  pole vault pole to know if the pole qualifies for
  the state track meet. He knows that the diameter
  of the bases are 6 inches and that the height is
  14 ft.
• The lateral area cant be more than 267(3204 in)
  square ft. Does his pole qualify for the track
  meet?

7
The lateral area cant be more than 267(3204 in)
square ft. Does his pole qualify for the track
meet?
6 in
L 2prh
Lateral Area of a Cylinder
L 2p(3)(168)
Substitution
14 ft
(168 in)
L 3166.7 in
Simplify
L 263.9 Ft
Divide
8
Example 1

• An office has recycling barrels for cans and
  paper. The barrels are cylindrical with cardboard
  sides and plastic lids and bases. Each barrel is
  3 feet tall, and the diameter is 30 inches. How
  many square feet of cardboard are used to make
  each barrel?

9
L 2prh
Lateral Area of Cylinder
30 In
r 15, h 36
L 2p(15)(36)
Use a Calculator
L 3392.9
3 Ft
(36) In
10
Surface Area of Cylinders

• To find the surface area of a cylinder, first
  find the lateral area and then add the areas of
  the bases. This leads to the formula for the
  surface area of a right cylinder.
• If a right cylinder has a surface area of T
  square units, a height of h units, and the bases
  have radii of r units, then T 2prh 2pr ²

r
h
11
Surface Area of a Cylinder
Find the surface area of the cylinder
T 2prh 2pr²
The radius of the base and the height of the
cylinder are given. Substitute these values in
the formula to find the surface area.
8.3
6.6
12
T 2prh 2pr ²
Surface Area of a Cylinder
T 2p(8.3)(6.6) 2p(8.3²)
r 8.3, h 6.6 Substitution
8.3
T 777.0 ft
Use a calculator
6.6
The surface area is approximately 777.0 square
feet
13
Find Missing Parts of the Equations

• Find the radius of the base of a right
  cylinder if the surface area is 128p square
  centimeters and the height is 12 centimeters

128p square centimeters
128p 2p(12)r 2pr ²
?
12 cm
14
T 2prh 2pr ²
Surface Area of a Cylinder
128p 2p(12)r 2pr ²
Substitution
128p 24pr 2pr ²
Simplify
64 12r r ²
Divide each side by 2p
0 r ² 12r - 64
Subtract 64 from each side
0 (r - 4)(r 16)
Factor
r 4 or -16
Since the radius of a circle cannot have a
negative value, -16 is eliminated. So the radius
of the base is 4 centimeters
15
A
g
t
Assignment
n

• Page six hundred fifty seven through page six
  hundred fifty eight.
• 657-658
• 9-20, 22-25, Omit 23

e
s
i
Good Luck!!!
s
n
m