7. History of Measurement
Classroom Activity (Page 196)
Measure the items listed on page 196
using original body parts that underlay
the measurement units listed. Record
the measurements made by each
person on the board and compare them.
12. Units of Measure
Metric & Imperial Rulers
•The following diagram shows a small ruler
with the common metric (centimetres) and
imperial (inches) units of linear
measurement.
20. Unit Conversion
Metric
•10 mm = 1 cm
•100 cm = 1 m
•1000 m = 1 km
Imperial
•12 inches = 1 foot
•36 inches or 3 feet = 1 yard
•5280 feet or 1760 yards = 1 mile
21. Unit Conversion
Unit Conversion Ratio
To convert a measurement given in
one unit of measure to another unit
of measure, a unit conversion ratio
can be used. A unit conversion ratio
is a fraction equal to 1.
22. Unit Conversion
Unit Conversion Ratio
Examples of unit conversion ratios taken
from the table on the previous slide are:
The conversion factor can be written with
either value in the numerator or the
denominator. For example:
23. Unit Conversion
Unit Conversion Ratio
When converting between units of measure, it is
best to write the conversion factor as follows:
• The numerator of the ratio consists of the required
unit of measure (the unit to which you want to
convert).
• The denominator of the ratio consists of the given
unit of measure (the original units in which the
measurement was taken).
24. Unit Conversion
Example 1
You purchase 485 cm of wire, however it is
sold by the meter. How many meters of
wire must you purchase?
35. Surface Area
• What does it mean to you?
• Surface area is found by finding
the area of all the sides and then
adding those answers up.
• How will the answer be labeled?
• Units2 because it is area!
37. Find the SA of a Rectangular Solid
A rectangular solid has 6 faces.
Top
They are: Top
Bottom
Front
Right Back
Side
Front Right Side
Left Side
We can only see 3 faces at any one time.
Which of the 6 sides are the same?
Top and Bottom
Front and Back
Right Side and Left Side
38. Surface Area of a Rectangular Solid
We know that
Each face is a rectangle.
Top and the
Formula for finding the area of a
Right
rectangle is:
Side A = lw
Front
Steps:
Find:
Area of Top
Area of Front
Area of Right Side
Find the sum of the areas
Multiply the sum by 2.
The answer you get is the surface area of the rectangular solid.
39. Find the Surface Area of the following:
Find the Area of each face: 12 m
2
Top 5m
A = 12 m x 5 m = 60 m
Top
Right
Side
8m Front Front 8m
A = 12 m x 8 m = 96 m
2
5m 12 m
12 m
2 2 2 2
Sum = 60 m + 96 m + 40 m = 196 m Right 2
Side 8m A = 8 m x 5 m = 40 m
2 2
Multiply sum by 2 = 196 m x 2 = 392 m
5m
2
The surface area = 392 m
40. Find the Surface Area
Area of Top = 6 cm x 4 cm = 24
2
cm 2
24 m
2
Area of Front = 14 cm x 6 cm = 84 cm
2
Area of Right Side = 14 cm x 4 cm = 56 cm
2
2
56 m Find the sum of the areas:
14 cm 84 m
2 2 2 2
24 cm + 84 cm + 56 cm = 164 cm
Multiply the sum by 2:
4 cm
2 2
6 cm 164 cm x 2 = 328 cm
The surface area of this
2
rectangular solid is 328 cm .
41. Nets
A net is all the surfaces of a rectangular solid laid out flat.
Back 8 cm
Top
Left Side Top Right Side 5 cm
Right 8 cm
Side
Front
8 cm
Front 8 cm
5 cm
10 cm
5 cm
Bottom
10 cm
42. Find the Surface Area using nets.
Top
Back 8 cm
Right
Side
Front
8 cm
Left Side Top Right Side 5 cm
5 cm
8 cm
10 cm
Front 8 cm
Each surface is a rectangle. 80
A = lw
80
5 cm
Find the area of each surface. Bottom
Which surfaces are the same? 10 cm 40
Find the Total Surface Area. 50 50 40
What is the Surface Area of the Rectangular solid?
2
340 cm
44. Problem of the Day
How can you cut the rectangular prism
into 8 pieces of equal volume by making
only 3 straight cuts?
45. Problem of the Day
How can you cut the rectangular prism
into 8 pieces of equal volume by making
only 3 straight cuts?
46. What is volume and capacity?
Volume is the quantity of three-dimensional space
enclosed by some closed boundary, for example, the space
that a substance or shape occupies or contains.
The volume of a container is generally understood to be
the capacity of the container, that is the amount of fluid
that the container could hold.
47.
48. Warm Up
Identify the figure described.
1. two triangular faces and the other faces in the
shape of a parallelograms
2. one hexagonal base and the other faces in the
shape of triangles
3. one circular face and a curved lateral surface
that forms a vertex
49. Warm Up
Identify the figure described.
1. two triangular faces and the other faces in the
shape of a parallelograms triangular prism
2. one hexagonal base and the other faces in the
shape of triangles hexagonal pyramid
3. one circular face and a curved lateral surface that
forms a vertex cone
51. Volume of a Prism
h
V Bh
Volume
Base Area Height
Base Area
Remember the “Base Area” formula will be determined
by the base shape.
52. Example #1: Finding the Volume of a Prism
Find the volume of the regular rectangular prism.
V Bh
B (4)(12)
V (48)(12)
3
V 576 ft
53. Volume of a Cylinder
Base Area
Radius V Bh
Volume Base Area Height
h
2
B r
Base Radius
Area
54. Example #2
Finding the Volume of a Cylinder
Find the volume of a cylinder with height 10 cm
5 cm
and radius 5cm.
V Bh 10 cm
2
B r
2
B (5)
2
B 25 cm
V 25 (10)
3
V 250 cm
55. Volume of a Pyramid
1
V Bh
B Volume
3
Base Area Height
56. Example #3 Finding Volume of a Pyramid
Find the volume of a square pyramid with base edges 5
m and height 3 m.
1 3m
V Bh
3
B s2
B 52
2 5m
B 25 m
1
V (25)(3)
3
3
V 25 m
57. Volume of a Cone
1
V Bh
Volume
3
Height
Base Area
r
B
58. Example#4
Finding the Volume of a Cone
The radius of the base of a cone is 6 m. Its height is 13 m.
Find the volume.
1
V Bh
3 13 m
B r2
2
B 6
B 36 m 2 6m
1
V (36 )(13)
3
3
V 156 m
60. A sphere is a 3D figure that is
circular in shape, e.g., a ball. All
points on the sphere are equidistant
from a single point inside the sphere
called the centre.
62. Volume of a Sphere
2(Volume (cone)) = Volume (sphere)
2X
=
2(Area of Base ) (height) /3= Volume (sphere)
2( r2 )(h)/3= Volume (sphere) r
h
BUT h = 2r r
2( r2)(2r)/3 = Volume(sphere)
4( r3)/3 = Volume(sphere)
63. Volume of a Sphere
3
4 r
Volume sphere
3
4 r 3
3
64. Find the volume and surface area of
a sphere with radius 12 cm.
Volume = (4/3)πr3
Hinweis der Redaktion
This template can be used as a starter file for presenting training materials in a group setting.SectionsRight-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors.NotesUse the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production)Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale.Graphics, tables, and graphsKeep it simple: If possible, use consistent, non-distracting styles and colors.Label all graphs and tables.
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Give a brief overview of the presentation. Describe the major focus of the presentation and why it is important.Introduce each of the major topics.To provide a road map for the audience, you can repeat this Overview slide throughout the presentation, highlighting the particular topic you will discuss next.
Give a brief overview of the presentation. Describe the major focus of the presentation and why it is important.Introduce each of the major topics.To provide a road map for the audience, you can repeat this Overview slide throughout the presentation, highlighting the particular topic you will discuss next.
This template can be used as a starter file for presenting training materials in a group setting.SectionsRight-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors.NotesUse the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production)Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale.Graphics, tables, and graphsKeep it simple: If possible, use consistent, non-distracting styles and colors.Label all graphs and tables.
Give a brief overview of the presentation. Describe the major focus of the presentation and why it is important.Introduce each of the major topics.To provide a road map for the audience, you can repeat this Overview slide throughout the presentation, highlighting the particular topic you will discuss next.
This is another option for an Overview slides using transitions.
Give a brief overview of the presentation. Describe the major focus of the presentation and why it is important.Introduce each of the major topics.To provide a road map for the audience, you can repeat this Overview slide throughout the presentation, highlighting the particular topic you will discuss next.
