Transcript PowerPoint Presentation - Unit 1 Module 1 Sets, elements

Part 3 Module 6
Units of Measure in Geometry
Part 3 Module 6
Units of Measure in Geometry
Next Tuesday all four parts of your finals week
homework project will be posted. We will discuss
the details at that time.
The first of the four parts will cover geometry (Part 3
Modules 7 through 9), the topic that we will cover
over the last two weeks of class.
As a preliminary to discussing geometry, we spend a
moment in Part 3 Module 6, reviewing some basic
facts about units of measure.
Part 3 Module 6 will be included on Test 3.
Linear Measure
Linear measure is the measure of distance.
For instance, lengths, heights, and widths of geometric
figures are distances, as are the radius, diameter and
circumference of a circle. The perimeter of a figure is
another example of distance.
Distance is measured in linear units, such as inches,
feet, yards, miles, meters, centimeters, millimeters
and kilometers.
Converting Linear Units
In the United States, any educated person should be aware of the
following relationships among basic units of linear measure in the
English system (inches, feet, yards, miles), and among the basic
units of linear measure in the metric system (meters, centimeters,
millimeters, kilometers).
1 foot = 12 inches
1 yard = 3 feet
1 yard = 36 inches
1 mile = 5280 feet
1 meter = 1000 millimeters
1 meter = 100 centimeters
1 kilometer =1000 meters
Multiply or divide
Referring to the conversion factors on the
previous page, we convert from larger units
to smaller units by multiplying (for instance,
to convert from yards to inches we multiply by
36); we convert from smaller units to larger
units by dividing (for instance, to convert
from centimeters to meters we divide by 100).
Examples
1. How many meters are in 3 kilometers?
2. How many miles are in 20,000 feet?
Answers
1. To convert 3 kilometers to meters we multiply by 1000.
3 x 1000 = 3000 m in 3 km
2. To convert 20000 feet to miles we divide by 5280.
20000/5280 = 3.88 miles in 20000 ft.
Square Measure
Square units (such as square inches or square
centimeters) are used to describe the area of a
two-dimensional figure.
Area is the amount of 2-dimensional space
covered by a flat object.
To understand the difference between linear
measure and square measure, and to correctly
convert between square units, you must
realize that one square unit is the area of a
square that is 1 unit long and 1 unit wide.
Exercise #1
(From The BIG UNIT-izer
www.math.fsu.edu/~wooland/unitizer.html )
How many square inches are in 9 square feet?
A. 0.75
B. 108
C. 0.063
D. 1296
Solution #1
How many square inches are in 9 square feet?
A. 0.75
B. 108
C. 0.063
D. 1296
The answer is not B, because the question is not asking
for the number of inches in 9 feet.
Square inches and square feet are different from inches
and feet.
To answer correctly, we must first find the correct
conversion factor when converting between square
feet and square inches.
Solution #, page 2
We must find the correct conversion factor when converting between square feet and
square inches.
This will depend upon the fact that one foot equals 12 inches, and also upon the
meaning on “square.”
“One square foot” means literally one foot times one foot.
1 sq. ft = 1 ft. x 1 ft.
= 12 in. x 12 in
= 144 sq. in.
We have figured out that to convert between square feet and square inches, the
correct factor is 144, not 12.
So, to convert 9 sq. feet to sq. yards, we multiply by 144.
9 x 144 = 1296. The correct choice is D.
Illustration
The figure below illustrates why 1 square foot = 144 square inches.
1 foot
1 square foot
One foot equals 12 inches
1 square inch
1 foot
1 foot
One square foot
equals 144
square inches
Cubic Units
Cubic units (such as cubic meters or cubic yards) are
used to describe the volume of a three-dimensional
figure.
Volume is the amount of 3-dimensional space occupied
by a solid object, for instance, or the amount of fluid that
can be contained in a hollow vessel.
Exercise #2
How many cubic yards are in 150 cubic feet?
A. 16.667
B. 450
C. 50
D. 5.556
Solution #2
How many cubic yards are in 150 cubic feet?
A. 16.667
B. 450 C. 50
D. 5.556
The answer is not C, because we are not converting feet
to yards. We are converting cubic feet to cubic yards.
We must find the correct factor for converting between
cubic yards and cubic feet.
This will depend upon the fact that one yard equals three
feet, and the meaning of the word “cubic.”
Solution #2, page 2
“One cubic yard” means literally one yard times one yard
times one yard.
1 cubic yard = 1 yard x 1 yard x 1 yard
= 3 feet x 3 feet x 3 feet
= 27 cubic feet
We have figured out that the correct conversion factor is
1 cubic yard = 27 cubic feet.
So, to convert 150 cubic feet to cubic yards, we divide by
27.
150/27 = 5.556
The correct choice is D.
Illustration
The figure below illustrates why 1 cubic yard equals 27
cubic feet.