Customary Units of Measurement

Transcription

1 Customary Units of Measurement What would it be like to have no system of measurement? If we are to measure something, we need a unit of measure. standard unit of measure: one that people have agreed to use length - inches, feet, yards, miles 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (36 inches) 1 mile (mi) = 1760 yards (5,280 feet) weight - ounces, pounds, tons 1 pound (lb) = 16 ounces (oz) 1 ton (T) = 2,000 pounds liquid volume - ounces, cup, pint, quart, gallon 1 cup (c) = 8 fluid ounces (fl oz) 1 pint (pt) = 2 c (16 fl. oz.) 1 quart (qt) = 2 pints (4 c) (32 fl. oz.) 1 gallon (gal) = 4 qt (8 pt) (16 c) (128 fl.oz.) Is there a pattern in the way that the units are related to one another? No (because of this it has some disadvantages) Converting from one measure to another: (1) from a larger unit to a smaller unit first determine the number of times the smaller unit is contained in the larger unit then multiply the given measure by this number example: 14 yards into feet 3 ft = 1 yd 14 x 3 = 42 feet (2) from a smaller unit to a larger unit first determine the number of times the smaller unit is contained in the larger unit then divide the given measure by this number example: 72 in =? yd 36 in = 1 yd 72/36 = 2 yd Metric System The major disadvantage of our English system of measurement is that the units are not related to one another. The metric system does have related units and it's easy to use. (Metric system is based on powers of 10.) Metric standard units: length/distance - meter (m) sometimes spelled metre weight/mass - gram (g) liquid volume - liter (l ) sometimes spelled litre

2 Metric prefixes (each prefix represents a different power of 10) (the prefixes show the relationship between the derived unit and the basic unit) (the same prefixes are used with the meter, the gram, and the liter) kilo - one thousand k hecto - one hundred h deka - ten dk Standard Unit of Measure (one) m or g or l deci - one-tenth d centi - one-hundredth c milli - one-thousandth m Several hundred years ago scientists defined a meter as one ten-millionth of the distance from the North Pole to the equator. Now scientists define the meter in terms of wavelengths of light. k h dk d c m (If you go up the scale, you are moving from a smaller unit to a larger unit and you divide; therefore you move the decimal to the left.) (If you go down the scale, you are moving from a larger unit to a smaller unit and you multiply; therefore you move the decimal to the right.) Perimeter perimeter of a figure: the distance around the figure perimeter of a polygon: the sum of the lengths of its sides per - "around" meter - "measure" TRIANGLE P = a + b + c (1) 5", 7", and 9" P = 21 inches (2) 10", 1 ft., 14" P = 36 inches (3) P = 24.2 feet sides = 6.4 feet and 9.7 feet other side =? 8.1 feet ISOSCELSE TRIANGE P = 2a + b (4) sides = 9.5 cm and base = 15 cm P = 34 cm (5) P = 30 yards base = 14 yards sides =? 8 yards EQUILATERAL TRAINGE P = 3s (6) s = 125 ft. P = 375 feet

3 (7) P = 18 m s =? 6 m RECTANGLE P = 2b + 2h or P = 2 (b + h) (8) = 8.9" w = 6.7" P =? 31.2" (9) P = 14 ft. = 4 ft. w =? 3 feet SQUARE P = 4s (10) s = 10 1/2 in. P = 42 inches (11) P = 33 feet s = 8.25 feet PARALLELOGRAM P = 2a + 2b (12) a = 10 dm b = 1.4 m (14 dm) P =? 48 dm or 4.8 m Area of Polygons one-dimensional object: LINE - numerical measurement called LENGTH two-dimensional object: POLYGON - numerical measurement called AREA three-dimensional object: PRISM - numerical measurement called VOLUME AREA: the amount of surface in a closed region (the number of square units needed to cover the region completely) It is measured in square units. (Dimensions must be expressed in the SAME units.) Area of a Rectangle: A = bh b - means base h - means height (why this formula works - they are taking the number of rows times the number of columns) Area of a Square: A = s2 (s x s) Area of a Parallelogram: A = bh Area of a Triangle: A = 1/2 bh or A = bh/2 height of a triangle - a line segment drawn from any vertex perpendicular to the line containing the opposite side (any triangle has 3 heights and 3 bases) Area of a Trapezoid: A = 1/2 h (b1 + b2)

4 Circles Circle: the set all points equidistant from a center point Naming a circle - name by the center point Radius (r): a segment that joins the center to a point on the circle All radius of a circle are congruent. Chord: a segment whose end points lie on a circle Diameter (d): a chord which contains the center (a segment that goes through the center and has its endpoints on the circle) Circumference (C): the distance around the circle What is the relationship between radius and diameter? C =?d or C = 2?r A =?r Surface Area Prism: a polyhedron with at least two faces that are congruent and parallel. Surface Area: the total area of the surfaces of a solid (1) Lateral Area (L.A.) - the sum of the areas of the lateral faces (sides - not the top and the bottom) (2) Total Area (T.A.) - the sum of the areas of all the faces (sides plus the top and the bottom) RECTANGULAR SOLID (one kind of prism) find the area of each side L.A. = ph p = perimeter of the base L.A. = (2a + 2b)h h = height of the prism L.A. = (2x6 + 2x10)x5 L.A. = ( )5 L.A. = (32)5 L.A. = 160 sq. ft. T.A. = L.A. + 2B B = area of the base

5 T.A. = (bh) T.A. = (6x10) T.A. = (60) T.A. = T.A. = 280 sq. ft. TRAINGULAR PRISM find the area of each side L.A. = ph L.A. = (a + b + c)h L.A. = ( )4 L.A. = (24)4 L.A. = 96 sq. yd. T.A. = L.A. + 2B T.A. = L.A. + 2( 1/2 bh) T.A. = ( 1/2 x 8 x 6) T.A. = T.A. = 144 sq. yd. CIRCULAR CYLINDER find the area of each side L.A. = Ch L.A. = (2 pi r)h L.A. = 2(3.14)(4)(12) L.A. = sq. m. T.A. = L.A. + 2B T.A. = L.A. + 2( pi r2) T.A. = (3.14)(42) T.A. = T.A. = sq. m Volume volume: the amount of space in a solid figure (measured in cubic units) Rectangular Solid

6 V = (bh)h V = (6 x 10) x 5 V = 60 x 5 V = 300 cu. ft. TRIANGULAR PRISM V = (1/2 bh)h V = (1/2 x 8 x 6) x 4 V = (24)4 V = 96 cu. yd. CIRCULAR CYLINDER V = ( pi r2)h V = (3.14 x 42) x 12 V = cu. m.