Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.2 Length, Area and Volume.
-
Upload
lorin-austin -
Category
Documents
-
view
220 -
download
2
Transcript of Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.2 Length, Area and Volume.
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
How to determine which unit of length is appropriateHow to determine which unit of area is appropriateCalculate areasHow to determine which unit of volume is appropriateCalculate volumes
8.2-2
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Length
The meter (metre) is used to measure things that we normally measure in yards and feet. Kilometer is used to measure things that we normally measure in miles.Centimeters and millimeters are used to measure what we normally measure in inches.
8.2-3
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Length
Centimeters and millimeters
Inches
8.2-4
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Choosing an Appropriate Unit of LengthDetermine which metric unit of length you would use to express the following.a) The height of the statueof Babe, Paul Bunion’sBlue Ox.
Meters
8.2-5
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Choosing an Appropriate Unit of Lengthb) The length of your nose
Millimeters or centimeters
c) The length of a fleaMillimeters
d) The height of the Empire State Building
Meters
8.2-6
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Choosing an Appropriate Unit of Lengthe) The diameter of a half-dollar
Millimeters or centimeters
f) The distance between Dallas, Texas, and Chicago, Illinois.
Kilometers
g) The diameter of a round wastepaper basket
Centimeters8.2-7
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Choosing an Appropriate Unit of Lengthh) The diameter of a pencil
Millimeters
f) Your waist sizeCentimeters
j) Your heightMeters or centimeters
8.2-8
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
AreaAreas are always expressed in square units: square centimeters, square kilometers, or square meters.
8.2-9
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
AreaSquare centimeter replaces square inches.Square meter replaces square foot or square yard.Square kilometer replaces square mile.One square kilometer is about 4/10 square mile.
8.2-10
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
AreaA hectare is a square unit 100 meters on each side (a square hectometer) and is symbolized ha.A hectare is about 2.5 acres.One square mile of land contains about 260 hectares.
8.2-11
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 2: Choosing an Appropriate Unit of AreaDetermine which metric unit of area you would use to measure the area of the following.a) Yellow StoneNational Park
Square kilometersor hectares
8.2-12
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 2: Choosing an Appropriate Unit of Areab) The top of a kitchen table
Square meters
c) The floor of a classroomSquare meters
d) A person’s property with an average-sized lot
Square meters or hectares
8.2-13
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 2: Choosing an Appropriate Unit of Areae) A newspaper page
Square centimeters
f) A baseball fieldHectares or square meters
g) An ice-skating rinkSquare meters
8.2-14
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 2: Choosing an Appropriate Unit of Areah) A dime
Square millimeters orsquare Centimeters
f) A lens in eyeglassesSquare Centimeters
j) A dollar billSquare Centimeters
8.2-15
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 4: Table TopFind the area of a rectangular table top if its length is 1.5 m and its width is 1.1 m.
Solution Use Area = length ×
width A = l × w A = 1.5 m × 1.1 m = 1.65 m2
8.2-16
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 5: A Circular TableA circular table has a diameter of about 76 cm. Find the surface area of the table.
SolutionUse A = πr2
π is approximately 3.14r = ½ diameter
A ≈ 3.14(38 cm)2
A ≈ 4534.16 cm2
8.2-17
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
When a figure has three dimensions: length, width and height, the volume can be found.The volume of an item can be considered the space occupied by the item.Volume of liquids can be expressed in terms of liters.
8.2-18
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
A liter is a little larger than a quart.Liters are used in place of pints, quarts, and gallons.A liter can be divided into 100 equal parts, each part is called a milliliter.Milliliters are used to express the volume of very small amounts of liquid.Drug doses are often expressed in ml.
8.2-19
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
The kiloliter is used to represent the volume of large amounts of liquid.Cubic meters are used to express the volume of large amounts of solid and gaseous material.
8.2-20
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
VolumeThe liquid in a liter container will fit exactly in a cubic decimeter.1l = 1000 ml and 1 dm3 = 1000 cm3
1l = 1 dm3 and 1 ml = 1 cm3
8.2-21
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
1 m3 = 1 kl
1 dm3 = 1 l
1 cm3 = 1 ml
Volume in LitersVolume in Cubic Units
8.2-22
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Choosing an Appropriate Unit of VolumeDetermine which metric unit of volume you would use to measure the volume of the following.a) The water in CraterLake (the deepestlake in the UnitedStates)
Kiloliters
8.2-23
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Choosing an Appropriate Unit of Volumeb) A carton of milk
Liters
c) A truckload of topsoilCubic meters
d) A liquid drug dosageMilliliters
8.2-24
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Choosing an Appropriate Unit of Volumee) Sand in a paper cup
Cubic centimeters
f) A dimeCubic millimeters
g) Water in a drinking glassMillimeters
8.2-25
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Choosing an Appropriate Unit of Volumeh) Water in a swimming pool
Kiloliters or liters or cubic meters
f) The storage area of a sports utility vehicle with the back seats folded down or removed
Cubic metersj) Concrete used to lay the
foundation for a basementCubic meters
8.2-26
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 7: Swimming Pool VolumeA swimming pool is 18 m long and 9 m wide, and it has a uniform depth of 3 m. Find (a) the volume of the pool in cubic meters and (b) the volume of water in the pool in kiloliters.
8.2-27
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 7: Swimming Pool Volume18 m long, 9 m wide, and depth of 3 m
Solutiona) Use V = l × w × h
= 18 m × 9 m × 3 m = 486 m3
b) 1 m3 = 1 kl, the pool will hold 486 kl
8.2-28
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 10: A Hot-Water HeaterA hot-water heater, in the shape of a right circular cylinder, has a radius of50 cm and a height of148 cm. What is the capacity, in liters, of the hot-water heater?
8.2-29
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 10: A Hot-Water Heaterradius of 50 cm and a height of 148 cm
SolutionUse V = πr2h
π is approximately 3.14We need to express the answer in liters so we will express the measurements in meters. The answer will be in cubic meters which can be converted to liters.50 cm = 0.5m, 148 cm = 1.48 m
8.2-30
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 10: A Hot-Water HeaterSolutionradius = 0.5 m and height = 1.48 m
Use V = πr2h V ≈ 3.14(0.5)2(1.48) V ≈ 3.14(0.25)(1.48) V ≈ 1.1618 m3
Convert to liters: 1 m3 = 1000 l1.1618 m3 = 1.1618 × 1000 = 1161.8 lThe hot-water heater’s capacity is about 1161.8 l.
8.2-31