slide1
Download
Skip this Video
Download Presentation
SURFACE AREA and VOLUME

Loading in 2 Seconds...

play fullscreen
1 / 96

SURFACE AREA and VOLUME - PowerPoint PPT Presentation


  • 142 Views
  • Uploaded on

SURFACE AREA and VOLUME. Solid Figures Introduction. CYLINDERS. PRISMS. PYRAMIDS. SPHERES. CONES. APPENDIX. SURFACE AREA and VOLUME. SOLID FIGURES. In a previous unit we discussed POLYGONS. . POLYGONS are 2-dimensional objects. . That means they have length and width, but no depth.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' SURFACE AREA and VOLUME' - shaman


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

SURFACE AREA and VOLUME

Solid Figures Introduction

CYLINDERS

PRISMS

PYRAMIDS

SPHERES

CONES

APPENDIX

slide2

SURFACE AREA and VOLUME

SOLID FIGURES

In a previous unit we discussed POLYGONS.

POLYGONS are 2-dimensional objects.

That means they have length and width, but no depth.

Like they are cut out of paper.

APPENDIX

MENU

slide3

SURFACE AREA and VOLUME

SOLID FIGURES

In this unit, we will learn about SOLIDS.

A SOLID is a 3-dimensional (3D) object.

That means it has length, width AND depth.

APPENDIX

MENU

slide4

SURFACE AREA and VOLUME

SOLID FIGURES

When the SOLID is made up of POLYGONS, it is called a POLYHEDRON

Each POLYHEDRON is made up of

Surfaces (called faces)

Segments (called edges)

Corners (called vertices)

APPENDIX

MENU

slide5

SURFACE AREA and VOLUME

SOLID FIGURES

Before we can do anything with SOLIDS, we must understand the difference between these shapes

There are many types of solids,

we are going to study the 5 basic types:

PRISM

PYRAMID

CYLINDER

CONE

SPHERE

APPENDIX

MENU

slide6

SURFACE AREA and VOLUME

SOLID FIGURES

To create a prism, draw any polygon you like.

PRISMS:

Next, draw another polygon, just like the first one

Connect the corresponding vertices

BASE

BASE

BASE

APPENDIX

MENU

slide7

SURFACE AREA and VOLUME

SOLID FIGURES

PRISMS:

APPENDIX

MENU

slide8

SURFACE AREA and VOLUME

SOLID FIGURES

PYRAMIDS:

Pyramids have one base

Instead of connecting to an identical base…

They connect to a point.

BASE

BASE

BASE

APPENDIX

MENU

slide9

SURFACE AREA and VOLUME

SOLID FIGURES

Pyramids:

APPENDIX

MENU

slide10

SURFACE AREA and VOLUME

SOLID FIGURES

When we name prisms and pyramids, we describe the base to tell what kind of prism or pyramid it is.

APPENDIX

MENU

slide11

SURFACE AREA and VOLUME

SOLID FIGURES

CYLINDERS:

A cylinder is like a prism…

But the bases are circles

APPENDIX

MENU

slide12

SURFACE AREA and VOLUME

SOLID FIGURES

Cylinders:

APPENDIX

MENU

slide13

SURFACE AREA and VOLUME

SOLID FIGURES

CONES:

A cone is a circular pyramid.

APPENDIX

MENU

slide14

SURFACE AREA and VOLUME

SOLID FIGURES

Cones:

APPENDIX

MENU

slide15

SURFACE AREA and VOLUME

SOLID FIGURES

SPHERES:

A sphere is a unique shape...

It has no base or sides or edges or vertices.

APPENDIX

MENU

slide16

SURFACE AREA and VOLUME

SOLID FIGURES

SPHERES:

APPENDIX

MENU

slide17

SURFACE AREA and VOLUME

SOLID FIGURES

Identify each of the following shapes as a

PRISM, PYRAMID, CYLINDER, CONE or SPHERE

#1

#2

#3

#4

SPHERE

CYLINDER

PRISM

#5

#6

PYRAMID

#7

CYLINDER

CONE

PYRAMID

#9

#10

#8

SPHERE

CONE & SPHERE

PRISM

APPENDIX

MENU

slide18

SURFACE AREA and VOLUME

SOLID FIGURES

So what are we going to do with these shapes?

We are going to calculate

SURFACE AREA and VOLUME

APPENDIX

MENU

slide19

SURFACE AREA and VOLUME

SOLID FIGURES

SUFARCE AREA:

Is literally the area of all the surfaces of a solid.

APPENDIX

MENU

slide20

SURFACE AREA and VOLUME

SOLID FIGURES

SUFARCE AREA:

Is literally the area of all the surfaces of a solid.

APPENDIX

MENU

slide21

SURFACE AREA and VOLUME

SOLID FIGURES

SUFARCE AREA:

Is literally the area of all the surfaces of a solid.

APPENDIX

MENU

slide22

SURFACE AREA and VOLUME

SOLID FIGURES

SUFARCE AREA:

Is literally the area of all the surfaces of a solid.

APPENDIX

MENU

slide23

SURFACE AREA and VOLUME

SOLID FIGURES

VOLUME:

Is the measure of how much “space” an object occupies.

It is often thought of as how much water an object can hold.

APPENDIX

MENU

slide24

SURFACE AREA and VOLUME

SOLID FIGURES

VOLUME:

Or how many cubic units it would take to fill an object

This is why volume is measured in CUBIC UNITS

Like:

Cubic feet:

ft3

Cubic centimeters cm3

APPENDIX

MENU

slide25

SURFACE AREA and VOLUME

PRISMS

A prism is a solid with 2 congruent BASES connected by LATERAL FACES

Lateral

face

APPENDIX

MENU

BASE

slide26

SURFACE AREA and VOLUME

PRISMS

To find the surface area of a PRISM, you can do it 2 ways:

Method 1:

Find the area of each shape that makes up the

Solid, and add them together

The front

2 x 10

= 20

12

The back

2 x 10

= 20

The left

6 x 10

= 60

10

60

The right

6 x 10

= 60

20

The top

2 x 6

= 12

The bottom

2 x 6

= 12

6

= 184

2

APPENDIX

MENU

slide27

SURFACE AREA and VOLUME

PRISMS

To find the surface area of a PRISM, you can do it 2 ways:

Method 2:

Use the formula for SURFACE AREA:

  • Identify the BASEs

(in a rectangular prism any pair of opposite sides can be bases)

  • Find the Area and Perimeter of the base

BASE

P; 16

A: 12

10

h: height of the prism

B: area of the base

10

6

P: perimeter of the base

2

12

16

APPENDIX

MENU

slide28

SURFACE AREA and VOLUME

PRISMS

Find the surface area of this regular decagonal prism:

Find the perimeter of the base

6+6+6+6+6+6+6+6+6+6

=60

Area of the bases

Lateral Area

A: 270m2

P:60m

6m

4m

APPENDIX

MENU

slide29

SURFACE AREA and VOLUME

PRISMS

Finding Volume is easier!

Find the VOLUME of this regular decagonal prism:

h: height of the prism

B: area of the base

A: 270m2

P:60m

6m

4m

APPENDIX

MENU

slide30

SURFACE AREA and VOLUME

PRISMS

RIGHT PRISMS vs OBLIQUE PRISMS

A right prism is a prism where the lateral faces are all perpendicular to the bases.

An oblique prism is a prism where the lateral faces are NOT perpendicular to the bases.

APPENDIX

MENU

slide31

SURFACE AREA and VOLUME

PRISMS

SUMMARY:

Things you need to know about a prism:

A prism has 2 bases

All the lateral faces are rectangles

Surface Area = 2B + ph

B is the area of the base

p is the perimeter of the base

h is the height of the prism

p x h gives the lateral area

Volume = B x h

B is the area of the base

h is the height of the prism

APPENDIX

MENU

slide32

SURFACE AREA and VOLUME

PRISMS

Find the…

3cm

…Surface Area

4cm

2cm

…Lateral Area

First we have to find that missing side

3cm

4cm

…Volume

Use the Pythagorean theorem

5cm

A:

P:

6cm2

12cm

APPENDIX

MENU

slide33

SURFACE AREA and VOLUME

PRISMS

Find the…

…Surface Area

3cm

4cm

5cm

2cm

…Lateral Area

…Volume

A:

P:

6cm2

12cm

APPENDIX

MENU

slide34

SURFACE AREA and VOLUME

PRISMS

Find the surface area and volume.

10

8

112

24

14

6

Area:

Perimeter:

136ft2

52ft

APPENDIX

MENU

slide35

SURFACE AREA and VOLUME

PRISMS

Find the volume.

APPENDIX

MENU

slide36

SURFACE AREA and VOLUME

PRISMS

Archimedes problem.

APPENDIX

MENU

slide37

SURFACE AREA and VOLUME

CYLINDERS

Since CYLINDERS are like prisms with circular bases,

We need to remember a few basic rules for circles.

APPENDIX

MENU

slide38

SURFACE AREA and VOLUME

CYLINDERS

Find the Circumference and area of the circle:

6in

12in

The red segment is the DIAMETER

We need the RADIUS

APPENDIX

MENU

slide39

SURFACE AREA and VOLUME

CYLINDERS

A CYLINDER is like a prism with circular bases

The surface area of a cylinder can be found with this formula

h: height of the cylinder

B: area of the base

Area of the bases

Lateral Area

C: circumference of the base

Most people find this formula easier:

APPENDIX

MENU

slide40

SURFACE AREA and VOLUME

CYLINDERS

Find the SURFACE AREA of this cylinder:

APPENDIX

MENU

slide41

SURFACE AREA and VOLUME

CYLINDERS

The VOLUME of a Cylinder:

The VOLUME of a cylinder can be found with this formula

h: height of the cylinder

B: area of the base

The expanded version of the formula:

APPENDIX

MENU

slide42

SURFACE AREA and VOLUME

CYLINDERS

Find the VOLUME of this cylinder:

APPENDIX

MENU

slide43

SURFACE AREA and VOLUME

CYLINDERS

SUMMARY

What you need to know about a cylinder:

  • A cylinder is a prism with circular bases
  • The lateral area is a rectangle
  • Surface Area:
  • Volume:
  • Lateral Area:

APPENDIX

MENU

slide44

SURFACE AREA and VOLUME

CYLINDERS

Find the Lateral Area, Surface Area and Volume:

11mm

9mm

APPENDIX

MENU

slide45

SURFACE AREA and VOLUME

CYLINDERS

Find the surface area and volume of this shape

31ft

8ft

16ft

31ft

If it was a complete cylinder:

What did we forget?

But we only want half of it

APPENDIX

MENU

slide46

SURFACE AREA and VOLUME

CYLINDERS

Find the surface area and volume of this shape

31ft

8ft

If it was a complete cylinder:

But we only want half of it

APPENDIX

MENU

slide47

SURFACE AREA and VOLUME

PYRAMIDS

A PYRAMID is a shape with a single base, where all the vertices of the base are connected to a single point (apex)

APPENDIX

MENU

slide48

SURFACE AREA and VOLUME

PYRAMIDS

Just like with prisms, we will need to find:

  • Base Perimeter
  • Base Area
  • Height of the pyramid

However, with pyramids, we will also need to find a different measurement…

height

Slant height

…SLANT HEIGHT

APPENDIX

MENU

slide49

SURFACE AREA and VOLUME

PYRAMIDS

Slant height is the distance someone would travel walking up the OUTSIDE of a pyramid.

SLANT HEIGHT

APPENDIX

MENU

slide50

SURFACE AREA and VOLUME

PYRAMIDS

APPENDIX

MENU

slide51

SURFACE AREA and VOLUME

PYRAMIDS

Finding the SURFACE AREA of a PYRAMID

Rectangular Pyramid

L: Slant height

B: area of the base

P: perimeter of the base

25m

22m

22m

APPENDIX

MENU

slide52

SURFACE AREA and VOLUME

PYRAMIDS

Finding the SURFACE AREA of a PYRAMID

Rectangular Pyramid

25m

Lateral Area

22m

22m

Base Area:

Base Perimeter:

484m2

88m

APPENDIX

MENU

slide53

SURFACE AREA and VOLUME

PYRAMIDS

Finding the VOLUME of a PYRAMID

Rectangular Pyramid

h: height

B: area of the base

11ft

8ft

10ft

Base Area:

Base Perimeter:

80ft2

36ft

APPENDIX

MENU

slide54

SURFACE AREA and VOLUME

PYRAMIDS

SUMMARY:

Things you need to know about a pyramid:

A pyramid has only 1 base

All the lateral faces are triangles

Surface Area =

B is the area of the base

p is the perimeter of the base

l is the slant height of the pyramid

½ x p x l is the lateral area

Volume =

B is the area of the base

h is the height of the prism

h

l

APPENDIX

MENU

slide55

SURFACE AREA and VOLUME

PYRAMIDS

Hey, I need to know the height.

Hey, I need to know the slant height.

15

20

24

16

APPENDIX

MENU

slide56

SURFACE AREA and VOLUME

PYRAMIDS

Find the Lateral Area, Surface area and Volume:

Lateral Area

B:

P:

400

80

APPENDIX

MENU

slide57

SURFACE AREA and VOLUME

PYRAMIDS

Find the Lateral Area, Surface area and Volume:

B:

P:

400

80

APPENDIX

MENU

slide58

SURFACE AREA and VOLUME

PYRAMIDS

Find the Lateral Area, Surface area and Volume:

h

10

B:

P:

400

80

APPENDIX

MENU

slide59

SURFACE AREA and VOLUME

PYRAMIDS

Find the Volume:

APPENDIX

MENU

slide60

SURFACE AREA and VOLUME

CONES

A CONE is basically a pyramid with a circular base

APPENDIX

MENU

slide61

SURFACE AREA and VOLUME

CONES

R: radius

H: height

L: slant height

Lateral Area

L

H

R

APPENDIX

MENU

slide62

SURFACE AREA and VOLUME

CONES

Find the surface area and volume for the cone shown:

Find the slant height with the Pythagorean Theorem

13

12in

5in

APPENDIX

MENU

slide63

SURFACE AREA and VOLUME

CONES

Find the surface area and volume:

APPENDIX

MENU

slide64

SURFACE AREA and VOLUME

CONES

Find the Lateral Area:

Lateral Area

5

APPENDIX

MENU

slide65

SURFACE AREA and VOLUME

CONES

Find the Volume:

TOTAL:

Cylinder:

Cone:

APPENDIX

MENU

slide66

SURFACE AREA and VOLUME

SPHERES

A sphere is just a ball.

It has 1 important measurement, that is used to find all its other properties

R

The RADIUS R

Official definition of a SPHERE:

The collection of all points in space that are the same distance (radius) from a point (center).

APPENDIX

MENU

slide67

SURFACE AREA and VOLUME

SPHERES

12m

APPENDIX

MENU

slide68

SURFACE AREA and VOLUME

SPHERES

Find the surface area:

8 in.

APPENDIX

MENU

slide69

SURFACE AREA and VOLUME

SPHERES

Find the volume:

2 ft.

APPENDIX

MENU

slide70

SURFACE AREA and VOLUME

SPHERES

Find the volume and surface area of the hemisphere:

10in

Half the sphere

+

the circle

APPENDIX

MENU

slide71

SURFACE AREA and VOLUME

SPHERES

Find the volume and surface area of the hemisphere:

10in

We only want half

APPENDIX

MENU

slide72

SURFACE AREA and VOLUME

SPHERES

Find the volume:

Cone:

Ice cream:

TOTAL:

APPENDIX

MENU

slide73

SURFACE AREA and VOLUME

APPENDIX

OPENERS

REVIEWS

ASSIGNMENTS

MENU

slide74

SURFACE AREA and VOLUME

OPENERS

ABCDEFGHIJKLMNOPQRSTU

APPENDIX

MENU

slide75

SURFACE AREA and VOLUME

OPENERS

A

APPENDIX

MENU

slide76

SURFACE AREA and VOLUME

OPENERS

B

APPENDIX

MENU

slide77

SURFACE AREA and VOLUME

OPENERS

C

APPENDIX

MENU

slide78

SURFACE AREA and VOLUME

OPENERS

D

APPENDIX

MENU

slide79

SURFACE AREA and VOLUME

OPENERS

E

APPENDIX

MENU

slide80

SURFACE AREA and VOLUME

OPENERS

F

APPENDIX

MENU

slide81

SURFACE AREA and VOLUME

OPENERS

G

APPENDIX

MENU

slide82

SURFACE AREA and VOLUME

OPENERS

h

APPENDIX

MENU

slide83

SURFACE AREA and VOLUME

OPENERS

I

APPENDIX

MENU

slide84

SURFACE AREA and VOLUME

OPENERS

J

APPENDIX

MENU

slide85

SURFACE AREA and VOLUME

OPENERS

K

APPENDIX

MENU

slide86

SURFACE AREA and VOLUME

OPENERS

L

APPENDIX

MENU

slide87

SURFACE AREA and VOLUME

OPENERS

M

APPENDIX

MENU

slide88

SURFACE AREA and VOLUME

OPENERS

N

APPENDIX

MENU

slide89

SURFACE AREA and VOLUME

OPENERS

O

APPENDIX

MENU

slide90

SURFACE AREA and VOLUME

OPENERS

P

APPENDIX

MENU

slide91

SURFACE AREA and VOLUME

OPENERS

Q

APPENDIX

MENU

slide92

SURFACE AREA and VOLUME

OPENERS

R

APPENDIX

MENU

slide93

SURFACE AREA and VOLUME

OPENERS

S

APPENDIX

MENU

slide94

SURFACE AREA and VOLUME

OPENERS

T

APPENDIX

MENU

slide95

SURFACE AREA and VOLUME

REVIEWs

APPENDIX

MENU

slide96

SURFACE AREA and VOLUME

REVIEWs

APPENDIX

MENU

ad