English Measurement Relationships

Transcription

1 Math 30 Prealgebra Sec 10.1: Using Unit Fractions with U.S. and Metric Units Defn A unit fraction is a fraction that shows the relationship between units and is equal to 1. Ex English Measurement Relationships Length Weight 1 foot (ft) = 12 inches (in) 1 pound (lb) = 16 ounces (oz) 1 yard (yd) = 3 feet (ft) 1 ton (T) = 2000 pounds (lb) 1 mile (mi) = 5280 feet (ft) Capacity Time 1 cup (c) = 8 fluid ounces (fl oz) 1 minute (min) = 60 seconds (sec) 1 pint (pt) = 2 cups (c) 1 hour (hr) = 60 minutes (min) 1 quart (qt) = 2 pints (pt) 1 day = 24 hours (hr) 1 gallon (gal) = 4 quarts (qt) 1 week (wk) = 7 days Converting Among Measurement Units 1) Multiply when converting from a unit to a unit. ex 2) Divide when converting from a unit to a unit. Weight 1 kilogram kg = 1000 grams 1 gram g = the basic unit 1 milligram mg = gram Length Volume 1 kilometer km = 1000 meters 1 kiloliter kl = 1000 liters 1 meter m = the basic unit 1 liter L = the basic unit 1 centimeter cm = 0.01 meter 1 milliliter ml = liter 1 millimeter mm = meter gram Liter meter kilo hecto deka basic unit deci centi milli These prefixes identify units that are larger than the basic unit. These prefixed identify units that are smaller than the basic unit. kilo hecto deka Basic Unit deci centi milli Move LEFT Move RIGHT Prefix kilometer hectometer dekameter meter decimeter centimeter millimeter of a of a of a Meaning meters meters meters meter meter meter meter Symbol km hm dam/dm m dm cm mm Page 1 of 14

2 Ex 1 Convert. a) b) c) 84 in = ft 87 in = ft 2.25 lb = oz d) e) f) 11 days = hours 192 oz = lb 7 gal= qt Ex 2 Judy is making a wild mushroom sauce for pasta tonight for a group of friends. She bought 26 ounces of wild mushroom at $6.00 per pound. How much did the mushrooms cost? Ex 3 Convert. a) b) c) 44 cm = mm 7.6 km = m 5261 ml = kl d) e) f) 5.9 kg = mg 18 ml = L = kl 12 DL = L Page 2 of 14

3 g) h) i) 0.84 cm = m = km 6 mi = ft 6 tons = lb j) k) l) 210 lb = T 15 ft = mi 3 oz = T Ex 4 A dam is 335 meters high. a) How many kilometers high is the dam? b) How many centimeters high is the dam? Sec 10.2: Converting Between the U.S. and Metric Systems U.S. to Metric Metric to U.S. Units of length 1 mile 1.61 kilometers 1 kilometer 0.62 mile 1 yard meter 1 meter 3.28 feet 1 foot meter 1 meter 1.09 yards 1 inch = 2.54 centimeters* 1 centimeter inch Units of volume 1 gallon 3.79 liters 1 liter gallon 1 quart liter 1 liter 1.06 quarts Units of weight 1 pound kilogram 1 kilogram 2.2 pounds 1 ounce grams 1 gram ounce *Exact value Page 3 of 14

4 Ex 5 Perform each conversion. Round your answer to the nearest hundredth if necessary. a) 12 km to mi b) 35 m to ft c) 19.6 cm to in d) 6.5 L to qt e) 6 kg to oz f) 142 cm to ft g) 60 kph to mph h) 40 mph to kmp i) to Fahrenheit j) to Celsius k) to Celsius l) to Fahrenheit Page 4 of 14

5 Ex 6 Solve. Round your answer to the nearest hundredth when necessary. a) The average weight for a 7-year-old girl is 22 kilograms. What is the average weight in pounds? b) A surgeon is irrigating an abdominal cavity after a cancerous growth is removed. There is a supply of 3 gallons of distilled water in the operating room. The surgeon uses a total of 7 liters of the water during the procedure. How many liters of water are left over after the operation? c) (calculator) While panning in a river, a prospector found a gold nugget that weighed oz. How many grams did the nugget weigh? Page 5 of 14

6 Sec 10.3: Angles The word for geometry comes from the Greek words for measure and earth. This is because geometry was originally used to measure land. Today we use geometry in many fields such as physics, drafting, art, engineering, and medicine. Terminology and Symbols point line line segment ray angle sides of angle vertex of angle We use degrees to measure the amount of opening of an angle. (Another form of measurement is radians.) Ex 7 Draw each and label the degrees. a) an angle that is a complete revolution b) an angle that is one-half a revolution c) an angle that is one-fourth a revolution The sides of the angle form lines. What symbol is used? Ex 8 Give four different names for the angle. A x R T B y x D S C An angle that measures is called a straight angle. An angle whose measure is between and is called an angle. An angle whose measure is between and is called an angle. Consider two intersecting lines. Two angles opposite of one another are called angles. Two angles that share a common side are called adjacent angles. Page 6 of 14

7 Draw two parallel lines. What symbol is used? A line that intersects two or more lines at different points is called a transversal. Draw a transversal. Alternate interior angles are two angles that are on opposite sides of the transversal and between (inside) the other two lines. Identify the alternate interior angles. Corresponding angles are two angles that are on the same side of the transversal and are both above (or below) the other two lines. Identify the corresponding angles. Parallel Lines Cut By a Transversal If two parallel lines are cut by a transversal, then the measures of corresponding angles are equal and the measures of alternate interior angles are equal. Ex 9 measures. a) Find the supplement of. b) Find the complement of. Ex 10 Find. Ex 11 Find the measure and. y + y Ex 12 Find. 3x x 2 Page 7 of 14

8 List perfect squares. Know these perfect squares for test. Sec 10.4: Square Roots and the Pythagorean Theorem Defn The square root of a number is the number where = and. In symbols, =, if =. - indicates square root and is called a radical sign Note: The result upon taking the square root is always nonnegative. Ex 13 Find, where =. Ex 14 Simplify. (Find the square root and simplify.) a) b) c) d) 2 2 e) f) 3 ( 2 3 ) Ex 15 Find the length of the side of a square that has an area of 16 square feet. Page 8 of 14

9 Ex 16 You can use your calculator to estimate 2. Without your calculator, decide which two consecutive whole numbers 2 is between. Pythagorean Theorem In any right triangle, if c is the length of the hypotenuse and a and b are the lengths of the two legs, then a + b = c. b c a Ex 17 Find the unknown side of each right triangle using the given information. Give the exact answer then round answers to the nearest thousandth if necessary. a) b) c) = and = 2 = = = = Ex 18 Find the area of the shape below made up of a square and right triangle. 10 in. 6 in. Page 9 of 14

10 Ex 19 Barbara is flying her dragon kite on 32 yd of string. The kite is directly above the edge of a pond. The edge of the pond is 30 yd from where the kite is tied to the ground. How far is the kite above the ground? ground Sec 10.5: The Circle Defn A circle is a figure for which all points on the figure (circle) are at an equal distance form a given point. This given pint is called the center of the circle. The radius is a line segment from the center to a point on the circle. The diameter is a line segment across the circle that passes through the center. Defn The distance across the rim of a circle is called the circumference, C. Given any circle, if we take it s C circumference and divide it by its diameter, we get. (Greek letter) That is, and is a number d that s approximately equal to Radius and Diameter of a Circle Circumference of a Circle Area of Circle = 2 = = 2 = = Ex 20 Find the radius of a circle if the diameter is 5.2 cm. Page 10 of 14

11 Ex 21 Find the circumference of a circle with radius = 15 in. Provide both the exact answer and estimate. Ex 22 Jimmy s truck has tires with a radius of 30 in. How many feet does his truck travel if the wheel makes 9 revolutions? Ex 23 Mickey s car has tires with a radius of 15 in. He backed up his car a distance of 9891 in. How many complete revolutions did the wheels make backing up? Ex 24 Tom made a base for a circular patio by pouring concrete into a circular space 10 ft in diameter. Find the cost at $18 per square yard. Page 11 of 14

12 Sec 10.6: Volume The volume of a cylinder is the area of its circular base ( 2 (h). V r h, where r is the radius and h is the height. 2 r ) times the height The volume of a sphere is V 4 r 3 where r is the radius. 3 The volume of a cone is V r 2 h where r is the radius and h is the height. 3 The volume of a pyramid is Bh V, where B is the area of the base of the pyramid and h is the height. 3 Ex 25 Find each volume. a) A cylinder with radius 3 m and height 8 m. b) A sphere with radius 5 m. c) A cylindrical trash can with radius 1.05 ft and height 3.6 ft. d) A hemisphere with radius 6 m. Page 12 of 14

13 e) A cone with height 12 ft and radius 6 ft. f) A pyramid with height 10 m and a rectangular base measuring 8 m by 14 m. Ex 26 A collar of Styrofoam is made to insulate a pipe. Find the volume of the unshaded region (which represents the collar). The large radius R is the outer rim. The small radius r is the edge of the insulation. = = = 2 Sec 10.7: Similar Geometric Figures Similar means that the things being compared are alike in shape, even though they may be different in size. Examples of Similar Triangles Similar Triangles The corresponding angles of similar triangles are equal. The lengths of corresponding sides of similar triangles have the same ratio. The perimeters of similar triangles have the same ratios as the corresponding sides. That is: 2 = Page 13 of 14

14 Similar Figures The corresponding sides of similar geometric figures have the same ratio. Ex 27 Find the missing side. Provide the exact answer and also round to the nearest tenth when necessary. 25 cm 8 cm 75 cm n 3 in. n 15 in. 20 in. 3 in. Ex 28 Two triangles are similar. The larger triangle has sides 15 cm, 17 cm, and 24 cm. The 24-cm side on the larger triangle corresponds to a side of 9 cm of the smaller triangle. What is the perimeter of the smaller triangle? Ex 29 Thomas is rock climbing in Utah. He is 6 ft tall and his shadow measures 8 ft long. The rock he wants to climb casts a shadow of 610 ft. How tall is the rock he is about to climb? Page 14 of 14