Surface Area Powerpoint.ppt

(1)

Surface

Area

(2)

A formula is just a set of instructions. It

tells you exactly what to do!

All you have to do is look at the picture

and identify the parts.

(3)

Let

’

s start in the beginning…

Before you can do surface area or volume,

you have to know the following formulas.

Rectangle

A = lw

Triangle

A = ½ bh

Circle

A = π r²

(4)

Day 1 - Surface Area of

Prisms

Surface Area

= The

total area of the flat

surfaces

of a three-dimensional object

(Or think of it as the amount of paper you’ll

need to wrap the shape.)

• To calculate surface area simply find the area

_{To calculate surface area simply find the area}

of each face, then add the areas together

• Because you are finding the area of each face,

_{Because you are finding the area of each face,}

calculate your answer in units

(5)

Rectangular

Prism

Triangular

Prism

Prism = A solid object that has two

identical polygon bases and

rectangular shaped flat sides.

• _{Bases – are the shape you would}

have if you were to flatten the solid

• _{Height – the extended part of the}

(6)

Surface Area (SA) of a

Rectangular Prism

Like dice,

there are

six sides

(or 3 pairs

of sides)

1

st

pair

3

rd

pair

2

nd

(7)

(8)

• Add the area of all 6 sides to find the

_{Add the area of all 6 sides to find the}

aurface area.

10 - length

5 - width

6 - height

(9)

10 - length

5 - width

6 - height

Rectangular Prism Example

(continued)

Face Formula Area Top

(red,yellow)

b x h 10x5 = 50

Bottom b x h = 50 Front

(red,purple)

b x h 10x6 = 60

Back b x h = 60 Left

(yellow,purple)

b x h 6x5 = 30

Right b x h = 30 Total Surf.Area add = 280

units2

(10)

Practice

10 ft 12 ft

22 ft Face Formula Area

Top

(red,yellow)

b x h 22x10 = 220

Bottom b x h = 220 Front

(red,purple)

b x h 22x12 = 264

Back b x h = 264 Left

(yellow,purple)

b x h 10x12 = 120

(11)

Surface Area of a

Triangular Prism

•2 bases

(triangular)

•3 sides

(12)

Triangular Prism Net

(13)

2(area of triangle) + Area

of rectangles

15ft

Face Formula Area Front

(blue,black)

½ (b x h) ½ (12x15) = 90

Back ½ (b x h) = 90 Left

(yellow,red)

b x h 25 x 20 = 500

Right b x h = 500

Bottom (red,blue)

b x h 12 x 25 = 300

(14)

Practice

Face Formula Area

Front (blue, black)

½ (b x h) ½ (3 x 4) = 6

Back ½ (b x h) = 6 Left (blue,green) b x h 3 x 11 = 33 Right

(green,yellow)

b x h 11 x 5 = 55

Bottom (green,red)

b x h 11 x 4 =44

(15)

DAY 2

Surface Area of a

Cylinder

(16)

Review

•Surface area is like the amount of

paper you’ll need to wrap the shape.

•You have to “take apart” the shape

and figure the area of the parts.

(17)

Parts of a cylinder

A cylinder has 2 main

parts.

A

rectangle

(lateral

surface)

and

A

circle

– well, 2

circles really.

(18)

The Soup Can

Think of the Cylinder as a soup

can.

You have the top and bottom lid

(

circles

) and you have the label

(a

rectangle

– wrapped around

the can).

The lids and the label are related.

The circumference of the lid is

the same as the length of the

(19)

Area of the Circles

Formula for Area of Circle

A=

A= 

r

_r

2

2 = 3.14 x 3

_{= 3.14 x 3}

22

= 3.14 x 9

= 28.26

But there are 2 of them so

28.26 x 2 = 56.52 units

squared

(20)

The Rectangle (Lateral

(21)

Area of the Lateral

(22)

Add them together

Now add the area of the

circles and the area of

the rectangle together.

56.52 + 113.04

= 169.56

units

squared

The total Surface Area!

(23)

Formula for Cylinder

SA = (2



rh) + 2 (

_{rh) + 2 (}



r

_r

2

2 )

)

Label

_Label

Lids

_Lids

(2)

Area of Rectangle Area of

_{Area of Rectangle Area of}

Circles

(24)

Practice

Be sure you know the difference

between a radius and a diameter!

SA = (2

SA = (2

r h) + 2 (

_{r h) + 2 (}

r

_r

2

2 )

)

= (2x3.14 x 11 x 14) + 2 (3.14 x

11

2

2 )

)

= (967.12) + 2 (3.14 x 121)

= (967.12) + 2 (379.94)

= (967.12) + (759.88)

= 1727 cm

(25)

More Practice!

SA

= (2



rh) + 2 (



r

2

2 )

)

= (2 x 3.14 x 5.5 x 7) + 2 ( 3.14

x 5.5

2

2 )

)

= (241.78) + 2 (3.14 x 30.25)

= (241.78) + 2 (3.14 x 94.99)

= (241.78) + 2 (298.27)

= (241.78) + (596.54)

=

838.32 cm

2

2 11 cm

(26)

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Day 3

Surface Area of a

Pyramid

(28)

Pyramids

Like a prism, a pyramid has a polygon

shaped base but a pyramid is different

than a prism because it has triangular

faces.

(29)

Rectangular Pyramid

Nets

A pyramid has

2 shapes:

One (1) square

base &

Four (4)

triangle faces

(30)

Since you know how to find

the areas of those shapes

you can simply add them.

(31)

Square Pyramid

The base is a square

so all sides are 7.

Base (bottom) b x h 7 x 7 = 49

Left ½ (b x h) ½ (7 x 12) = 42 Right = 42

Front = 42

Back = 42

(32)

Rectangular

Pyramid

The base is a square

so all sides are 7.

Base (bottom) b x h 12 x 8 = 96 Left ½ (b x h) ½ (8 x 12) = 48 Right = 48

Front ½ (12 x 10)=60

Back = 60 Total Surf.Area =312

(33)

Triangular Pyramid Nets

A triangular

pyramid has 2

(34)

Triangular Pyramid

Base (bottom) ½ (b x h) ½ (17 x 14.7) = 124.95

Left ½ (b x h) ½ (17 x 13.8) = 117.3

Right = 117.3

Front = 117.3

(35)