6th Grade Math Textbook, Fundamentals

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Key Concept

Surface Area (S) of a Cylinder

S 2 r^2  2 rhwhere Ssurface area, rradius of

the circular base, and hheight of the cylinder.

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h

h

C  2 r

C  2 r

C  2 r

lateral bases

surface

h  9 in.

r  3 in. lateral surface

To find the surface area of the cylinder, use 3.14. bases

Total area of the circular bases: A 2 r^2

 2 (3)^2

 18 56.52 in.^2

Lateral Area: Aw(2r)(h)

 2 (3)(9)

 54 169.56 in.^2

S 18  54 

 72 

or

S56.52 169.56

226.08 in.^2

So the new designed label will be about 226.08 square inches.

Surface Area of Cylinders and Cones

Objective To draw and use nets to find the surface area of cylinders and cones

• To use formulas to find the surface area of cylinders and cones

A designer is creating a new label that will completely
cover a cylindrical carton. What is the surface area in
square inches of the new label?

To find the surface area of the label, find the surface area
of a cylinder.

The is the sum of the lateral

area and the area of the two congruent circular bases.

The is the area of the lateral

surface. The is the curved

surface that is not a base.

When the cylinder’s curved surface is completely

open, it takes the shape of a rectangle. Its length is

the circumference of the circular base and its width

is the height of the cylinder.

The area of the lateral surface of a cylinder is:

AwCh(2r)h 2 rh

The area of each circular bases is Ar^2.

The total surface area r^2 r^2  2 rh

 2 r^2  2 rh

lateral surface of a cylinder

lateral area of a cylinder

surface area of a cylinder

h  9 in.

r  3 in.

Remember:When you use either

3.14 or for , your answer will

be an approximation so you should

use the symbol. You can use the

symbol when you find surface

area in terms of .

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