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Surface Area of Cylinders

SURFACE AREA of a CYLINDER.

Imagine that you can open up a cylinder like so

You can see that the surface is made up of two

circles and a rectangle.

The length of the rectangle is the same as the

circumference of the circle!

EXAMPLE Round to the nearest TENTH.

Top or bottom circle A pr² A p(3.1)² A

p(9.61) A 30.2 cm²

Rectangle C length The length is the same as

the Circumference C p dC p(6.2)C 19.5

cm Now the area A lwA 19.5(12)A 234 cm²

Now add

30.2 30.2

234

SA 294.4 in²

Example 1

Rectangle

C 2?r

5 m

C 2(3.14)(5)

C 31.4 m

A lw

16 m

A 31.4(16)

A 502.4 m2

Area of the circles

Put the areas together

A ?r2

A 3.14(52)

S.A. 157 m2 502.4 m2

A 3.14 (25)

S.A. 659.4 m2

A 78.5 m2

2 circles 78.5 x 2 157 m2

EX2) S 2pr2 2prh

2p(42) 2p(4)(6)

80p in2 ? 251.2 in2

15 cm

EX3) S 2pr2 2prh

3 cm

2p(152) 2p(15)(3)

540p in2 ? 1695.6 cm2

Example 4)

A cylindrical soup can is 7.6 cm in diameter and

11.2 cm tall. What is the area of the label that

covers the side of the can?

Only the lateral surface needs to be covered.

L 2?rh

2?(3.8)(11.2)

Diameter 7.6 cm, so r 3.8 cm.

267.3 cm2

notes

Surface Area of Cylinders

- Date______________

SURFACE AREA of a CYLINDER.

Imagine that you can open up a cylinder like so

You can see that the surface is made up of two

circles and a rectangle.

The length of the rectangle is the same as the

circumference of the circle!

Example 1

Rectangle

5 m

16 m

Area of the circles

Put the areas together

EX2) S 2pr2 2prh

EX3) S 2pr2 2prh

Example 4)

A cylindrical soup can is 7.6 cm in diameter and

11.2 cm tall. What is the area of the label that

covers the side of the can?

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