![Page 1: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/1.jpg)
CHAPTER 5
MEASUREMENT
![Page 2: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/2.jpg)
SECTION 5-1
Ratios and Units of Measure
![Page 3: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/3.jpg)
MEASUREMENT– is a process used to find size,
quantities, or amounts
![Page 4: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/4.jpg)
COMPASS – is used for drawing curved lines and
circles for measuring distances.
![Page 5: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/5.jpg)
PROTRACTOR – is an instrument for measuring and
drawing angles.
![Page 6: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/6.jpg)
SCALES or RULERS – devices for measuring
distance.
![Page 7: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/7.jpg)
CALIPERS and MICROMETERS –
devices used for making precise measurements
![Page 8: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/8.jpg)
PRECISION – is related to the unit of measure
used.
![Page 9: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/9.jpg)
GREATEST POSSIBLE ERROR – is ½ the
smallest unit used to make the measurement.
![Page 10: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/10.jpg)
RATIO – is a quotient of two numbers that
compares one number with the other.
![Page 11: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/11.jpg)
RATE – is a ratio that compares two different
quantities
![Page 12: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/12.jpg)
UNIT RATE – compares a quantity to one unit of
that quantity
![Page 13: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/13.jpg)
SECTION 5-2
Perimeter, Circumference and Area
![Page 14: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/14.jpg)
PERIMETER – is the distance around a
polygon.
![Page 15: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/15.jpg)
CIRCUMFERENCE – is the distance around a
circle.
![Page 16: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/16.jpg)
AREA – the amount of surface a figure covers.
![Page 17: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/17.jpg)
Circle
C = d or 2rA =r2
![Page 18: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/18.jpg)
Rectangle or Square
P = 2l + 2wA = lw
![Page 19: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/19.jpg)
Triangle
A = ½bh
![Page 20: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/20.jpg)
Parallelogram
A = bh
![Page 21: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/21.jpg)
Trapezoid
A = ½h(b1+b2)
![Page 22: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/22.jpg)
SECTION 5-3
Probability and Area
![Page 23: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/23.jpg)
PROBABILITY – the likelihood that an event
will occur.
![Page 24: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/24.jpg)
P(any event) =number of favorable
outcomes ÷ number of possible outcomes
![Page 25: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/25.jpg)
SECTION 5-4
Problem Solving Skills: Irregular Shapes
![Page 26: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/26.jpg)
SECTION 5-5
Three-dimensional Figures and Loci
![Page 27: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/27.jpg)
POLYHEDRON– is a three-dimensional figure in which each surface is
a polygon and
![Page 28: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/28.jpg)
The surfaces are called faces. Two faces intersect at an edge, and a vertex is
a point where three or more edges intersect.
![Page 29: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/29.jpg)
PRISM - a polyhedron with two identical parallel
faces. Each of these faces is called a base and
![Page 30: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/30.jpg)
a prism is named by the shape of its bases.
![Page 31: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/31.jpg)
PYRAMID - a polyhedron with only one base. The other faces are triangles
that meet at a vertex and
![Page 32: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/32.jpg)
a pyramid is named by the shape of its base.
![Page 33: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/33.jpg)
LATERAL FACES - are those faces that are not
bases.
![Page 34: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/34.jpg)
LATERAL EDGES - are the edges of lateral faces
and can be parallel, intersecting,or skew.
![Page 35: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/35.jpg)
CYLINDER - a three-dimensional figure having a
curved region with two parallel congruent circular
bases. Its axis joins the centers of the two bases.
![Page 36: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/36.jpg)
CONE - a three-dimensional figure having a curved
surface and one circular base. Its axis is a segment
from the vertex to the center of the base.
![Page 37: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/37.jpg)
SPHERE - is the set of points in space that are the same distance from a given
point called the center of the sphere.
![Page 38: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/38.jpg)
SECTION 5-6
Surface Area of Three-dimensional Figures
![Page 39: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/39.jpg)
SURFACE AREA - The sum of the areas of all
the faces of a three-dimensional figure.
![Page 40: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/40.jpg)
FORMULAS
![Page 41: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/41.jpg)
Square base
A = s2
![Page 42: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/42.jpg)
Square prism
SA = 6s2
![Page 43: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/43.jpg)
Rectangular Prism
SA = 2(lw + lh + wh)
![Page 44: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/44.jpg)
Triangular face
A = ½bh
![Page 45: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/45.jpg)
Circular base
A = r2
![Page 46: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/46.jpg)
Curved surface
A = 2rh
![Page 47: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/47.jpg)
Cylinder
SA = 2rh + 2r2
![Page 48: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/48.jpg)
Cone
SA = rs + r2
S is the slant height
![Page 49: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/49.jpg)
Sphere
SA = 4r2
![Page 50: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/50.jpg)
SECTION 5-7
Volume of Three-dimensional Figures
![Page 51: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/51.jpg)
FORMULAS
![Page 52: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/52.jpg)
Prism
V = Bhwhere B = area of the
given base
![Page 53: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/53.jpg)
Pyramid
V = 1/3Bhwhere B = area of the
given base
![Page 54: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/54.jpg)
Cylinder
V = r2h
![Page 55: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/55.jpg)
Cone
V = 1/3r2h
![Page 56: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/56.jpg)
Sphere
V = 4/3r3
![Page 57: CHAPTER 5 MEASUREMENT SECTION 5-1 Ratios and Units of Measure](https://reader034.vdocuments.us/reader034/viewer/2022052312/56649ddd5503460f94ad4fd0/html5/thumbnails/57.jpg)
END