Calculating the Surface Area of a Cylinder

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Listen & Learn

PRESENTED BY CANADA GOOSE

Calculating The Surface

Area of a Cylinder

Mathematics, Grade 8

Surface Area of a Cylinder

Introduction

• Welcome to today’s topic

• Parts of Listen & Learn

 Presentation, questions, Q&A

• Housekeeping

 Your questions

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What you will learn

At the end of this lesson, you will be able to

• calculate the surface area of a cylinder by finding the area of the cylinder’s faces

• calculate the surface area of a cylinder using a formula

Agenda

• Cylinders in real life

• Review of concepts

• Properties of a cylinder

• Calculating area of a cylinder’s faces

• Calculating surface area of a cylinder using a formula

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Real-Life Applications

People in many professions calculate the surface area of cylinders.

Engineers tube production Manufacturers packaging

Designers painting

Contractors pipe construction

Agenda

• Review of concepts

• Calculating surface area of a cylinder’s faces

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Definitions and Terms

Area

The number of square units required to cover a 2D object.

Surface Area

The number of square units required to cover the surface area of a 3D object.

Definitions and Terms

Circumference

The distance around a circle.

Diameter

The distance across the centre of a circle.

circumference

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Definitions and Terms

Face

Polygons or 2D shapes of a 3D object. circular face of a cylinder

Pi (∏)

The ratio of the circumference of a circle to its diameter.

Pi is approximately equal to 3.14.

C ≈ 3.14 d

Definitions and Terms

Radius

Half the diameter of a circle.

Net

The 2D pattern of 3D shape.

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History

What is Pi?

Pi is the 16^th letter of the Greek

alphabet. It represents the ratio of the circumference of a circle to its diameter.

Pi is an infinite decimal.

This means that it never ends or repeats. It is approximately equal to 3.14.

π

Agenda

• Definitions and terms

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Definition

A cylinder is a 3D shape with two congruent circles for faces.

Labelling a Cylinder

• The circle faces of the cylinder are called the bases.

• The bases of the cylinder are congruent and parallel to each other.

• The perpendicular distance between the bases of the cylinder is the height.

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Question 1

The bases of a cylinder are:

a) congruent

b) parallel to each other c) circles

d) all of the above

Question 1

The bases of a cylinder are:

a) congruent

b) parallel to each other c) circles

d) all of the above

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Question 2

A cylinder’s height is which of the following measurements?

a) width of the cylinder’s base b) circumference of the cylinder

c) perpendicular distance between the cylinder’s bases

Question 2

A cylinder’s height is which of the following measurements?

a) width of the cylinder’s base b) circumference of the cylinder

c) perpendicular distance between the cylinder’s bases

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Agenda

Surface Area

The surface area of a cylinder is the number of square units

required to cover the entire surface of the cylinder.

surface area

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Calculating Surface Area

The area of a cylinder can be

calculated by reducing a cylinder to its net and finding the area of each shape in the net

cylinder = net of cylinder

Calculating Surface Area

two circles one

rectangle

A cylinder’s net consists of two circles and one rectangle.

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Calculating Surface Area

The surface area of a cylinder is calculated by adding the area of the cylinder’s two circles and one rectangle together.

Area of Circle 1 + Area of Circle 2 + Area of Rectangle

Surface Area of Cylinder

Calculating Surface

Area Example

Calculate the surface area of Cylinder A.

Cylinder A

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Calculating Surface

Area Example

Cylinder A = Net of Cylinder A

Height of cylinder = width of rectangle

Calculating Surface

Area Example

Cylinder A = Net of Cylinder A

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Calculating Surface Area

Example

Area of Circle 1

Area = Pi x radius² A = πr²

A = 3.14 x 5² A = 3.14 x 25 A = 78.5 cm²

Calculating Surface Area

Example

Area of Circle 2

Area = Pi x radius² A = πr²

A = 3.14 x 5² A = 3.14 x 25 A = 78.5 cm²

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Area of Rectangle

Area = length x width A = l x w

A = 31.4 x 20 A = 628 cm²

length = circumference of Circle 1 or 2

Calculating Surface Area

Example

Calculating Surface Area

Example

Where the length of the rectangle is the circumference or perimeter of Circle A or B, and the width is the height of the cylinder.

circumference of circle

= length of rectangle

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Calculating Surface Area

Example

Rectangle length calculation

Circumference = Pi x diameter C = πd

C = 3.14 x 10 C = 31.4 cm

Rectangle length = 31.4 cm

Calculating Surface Area

Example

Surface Area of Cylinder A

Area of Circle A 78.5 cm² + Area of Circle B 78.5 cm² + Area of Rectangle 628 cm²

Surface Area 785 cm²

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Question 3

What is the surface area of Cylinder B?

a) 500 cm² b) 471 cm² c) 207 cm²

a) 500 cm²

Question 3

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Question 3

Surface Area 78.5 + 78.5 + 314.0 471.0 cm² Length =

Circumference C = πd C = 3.14 x 10 C = 31.4 cm Circle 2

A = πr² A = 3.14 x 5² A = 3.14 x 25

A = 78.5 cm²

Surface Area Circle 1 + Circle 2 + Rectangle

Surface Area Rectangle

A = l x w A = 31.4 x 10 A = 314 cm² Circle 1

A = πr² A = 3.14 x 5² A = 3.14 x 25 A = 78.5 cm²

Calculating Surface Area

• Calculating the surface area by adding the area of the shapes of the cylinder is time consuming.

• By adding the formulas together surface area can be found more easily.

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Agenda

Formula

The formula to find the surface area of a cylinder is:

Area = 2 x pi x radius² + 2 x pi x radius x height or

A = 2πr² + 2πrh

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The formula for the area of a rectangle

Calculating Surface Area

with a Formula

Where:

2πr²+ 2πrh

The formula for the area of 2 circles

length = circumference cylinder net

Calculating Surface Area

with Formula Example

Calculate the surface area of the Cylinder C using a formula.

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Calculating Surface Area

with Formula Example

A = 2πr² + 2πrh

A = 2 x 3.14 x 3²+ 2 x 3.14 x 3 x 30 A = 6.28 x 9 + 6.28 x 3 x 30

A = 56.52 + 565.2 A = 621.72 m²

The surface area of Cylinder C is 621.72 m².

Calculating Surface Area

with Formula Example

Manny needs to cover the surface area of a cylinder with paper for a science project.

The cylinder is 20 cm tall and has a radius of 2 cm. How much paper

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Calculating Surface Area

with Formula Example

A = 2πr²+ 2πrh

A = 2 x 3.14 x 2² + 2 x 3.14 x 2 x 20 A = 6.28 x 4 + 6.28 x 2 x 20

A = 25.12 + 251.2 A = 276.32 cm²

Manny needs 276.32 cm² of paper to cover the cylinder.

Question 4

What is the surface area of Cylinder D?

a) 628 cm² b) 314 cm²

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Question 4

A = 2πr² + 2πrh A = 2 x 3.14 x 10² + 2 x 3.14 x 10 x 5 A = 6.28 x 100 + 6.28 x 10 x 5 A = 628 + 314 A = 942 cm²

The surface area of Cylinder D is 942 cm².

What is the surface area of Cylinder D?

a) 628 cm² b) 314 cm² c) 942 cm²

Question 5

Maria, an engineer, is creating a part for an airplane that is the shape of a cylinder.

The part is 2 metres high and has a

diameter of 2 metres. Maria needs to coat the part in plastic and therefore needs to calculate the surface area of the cylinder.

What is the surface area of the part?

a) 18.84 m²

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Maria, an engineer, is creating a part for an airplane that is the shape of a cylinder.

The part is 2 metres high and has a

diameter of 2 metres. Maria needs to coat the part in plastic and therefore needs to calculate the surface area of the cylinder.

What is the surface area of the part?

a) 18.84 m² b) 6.28 m² c) 50.24 m²

A = 2πr² + 2πrh : radius = ½ diameter A = 2 x 3.14 x 1² + 2 x 3.14 x 1 x 2 A = 6.28 x 1 + 6.28 x 1 x 2

A = 6.28 + 12.56 A = 18.84 m²

The surface area of the part is 18.84 m².

Question 5

Resources

Algebra Lab

www.algebralab.org/Word/Word.aspx?file=

Geometry_SurfaceAreaVolumeCylinders.xml

Mathwww.math.com/tables/geometry/surfareas .htm