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KEY Distance, Areas, Volumes-A sense of size and scale from the Electron to the Galaxies 1What is your estimate of the length of the front of our room? 30 FEET 2What is it measured in feet? 28ft 3What is the height of the room? 9 FEET 4What is length of the room? 30FEET(31ft measured) What is the area of the room(May use approximations)? 30x30=900 square feet If we need to tile the floor with one square foot tiles, how many tiles do we need? 900 What is the volume of the room? 30ft x30ftx9ft=8100cubic feet If you filled the room with water how many gallons would you need? How many cubic feet are in a gallon? .1337 cubic feet in a gallon. 8100/.1337=60,584gallons How many liters would you need? 3.78liters in a gallon. 60,584gallons x 3.78= 229,008 liters Distances Distances are one dimensional measurements. Distances are often measurements between two points in space. Length can be a measurement of the length, width or height of an object. American-English How many inches in a foot? 12 How many feet in a yard? 3 How many feet in a mile? 5280 Inches in yd? 36 Yards in a mile? 1760 How many miles from Los Angeles California to Washington DC? 2500miles How many miles around the equator? 25,000 miles How many miles to the moon? 250,000 miles How many miles to the Sun? 93 million miles What is that distance called? One Astronomical Unit What is the definition of a light year? The distance light travels in one year How far is a light year? 6 trillion miles(6x1012miles) 9x1012 kilometers Is a light year the distance from the Sun to the earth? NO WAY The closest star we see at night is Proxima Centauri. It is 4 light years away. How many miles away is that star? 4x6 trillion miles =24trillion miles (2.4x1013miles) The stars we see in the night sky are all from our galaxy-the Milky Way. The farthest object in the night sky is a smudge of light from our neighboring galaxy—the Andromeda Galaxy. Is our neighboring galaxy 2.5 light years away or 2.5 million light years away? Is a light year a distance or a time? The Andromeda Galaxy is 2.5 million light years away . A light year is a distance The average depth of the oceans , the depth in the earth where the temperature would cause water to boils-100C and the distance from LCS are all about the same . How many miles(nearest half mile) 2.5 miles The deepest hole in the earth is 7.5 miles dug in Russia. The deepest natural point on earth is in the oceans 6.8 miles . Where is that place and what is the geological form? The Marianna Trench . It is a place where two oceanic plates converge and the older denser plate subducts under the younger plate. The highest point on Earth is 29,500 feet(5.5 miles) Where is that and what is the land form. In the Himmalayan Mountains is Mount Everest. The Himmalayas were formed when the Indian continental plate converged with the Asian plate about 40 millon years ago forming this still growing mountain range. How deep is it to the center of the earth? 4000 miles or more exactly 6370 kilometers CONVERSIONS SI(Systeme Internationale)-American Is a meter closer to a foot (a ruler) or a yardstick? A yardstick What is a yard stick and a meter stick in inches? One Yard=36 inches. One meter =39.37 inches How many centimeters in an inch? 2.54 cm =inch A kilometer is a 1000 meters. Is a kilometer larger or smaller than a mile? It is smaller. A meter is close to a yard and we know 1000 yards are a lot less than a mile so we know a kilometer is less than a mile. 100 kilometers is how many miles? 61 miles So our general strategy when we hear “kilometers” is to multiply by .6 and we will get the approximate distance in miles. Distances(SI) (Use word and scientific notation) Divide a meter stick into a hundred units what measurement do you have? One centimeter=1 cm=10-2meters. A meter divided by a thousand is a millimeter=mm=10-3 meter. A meter divide by a million is the size of a bacteria cell. It is a micrometer==10-6meters A meter divided by a billion is the size of a cell membrane. It is a nanometer=nm=10-9meter. A meter divided by 10 billion is the diameter of an atom. It is an Angstrom=1 A=10-10meters A meter divided by a 1000 trillion is the diameter of the nucleus of an atom. It is a femtometer=fm=10-15meters. Areas Areas are two dimensional surfaces Draw a square inch-be accurate. How many square inches in a square foot? 144 How many square feet in a square yard? 9 Draw a diagram showing a square mile. What is a square mile called in surveying? One square mile is called a section. Diagram 5 is a square mile. How many acres in a square mile? 640acres Draw a square mile and divide it to show 320, 160 and 40 acres. See above Draw a football field and show how much is covered by an acre. Fill in from the goal line to the ten yard line of opposing team. That is an acre. 100 meters squared is 100 meters x 100 meters=10,000 square meters=hectare. I had this wrong on the worksheet. 100 square meters is 10 meters x 10 meters. It is NOT a hectare. A hectare is 10,000 sq. meters. (This is a common kind of mistake in terminology but you would expect that the teacher teaching units and areas would get it right.) Conversions How many acres in a hectare? 2.47 acres in a hectare Areas and Standard Shapes. Draw the shape, label sides or height and show formula for calculating the area. Square a2 Rectangle axb Triangle ½ bh Circle r2 Volumes Volumes are three dimensional measurements Teaspoons in a tablespoon. 3 tsp in a tblsp One Tablespoon=.5 oz Tablespoons in a cup 16 tbsp in a cup Ounces in a cup 8 oz in a cup Cups in a pint 2 cups in a pint Pints in a quart 2 pints in a quart Ounces in a quart 32 ounces in a quart Quarts in a gallon 4 quarts in a gallon SPECIAL AIDS FOR PROBLEM SOLVING 3dimensional measurements to volumes 0ne cubic foot= 7.5 gallons or 29.9 pints One gallon = .1337 gallons or 231 cubic inches Mass of one cu foot of H2O A Gallon = 3.78 liters=3,780ml=3780grams. 454 gm=pound 3780/454=8.32pounds so a gallon of H2O weighs 8.32 lb. A cubic foot of water has 7.5 gallons in it so it weighs 62.4 pounds. Lesson: Water Waves are Heavy Metric Conversions 1 tsp= 4.9 1 oz = 29.8 12 oz= 385 500 ml = 1 liter = ml ml ml 16.9 33.8 oz oz= 1.06 quarts Draw a milliter ml = cubic centimeter 10cmx10cmx10cm= 1000 cubic centimeters 1000cubic centimeters =One Liter Common Three dimensional Shapes (Volumes and Surface Areas) The volume is a three dimensional unit expressing how much space is taken up. The surface area is the area of needed to completely cover the outer surface of the shape. Volume Sphere 4/3R3 Cylinder R2h Surface Area 4R 2 2R2 +2Rh Cube a3 6a2 Rectangle axbxc 2ab+2ac+2bc Mass 1 cc of water = One gram 1 liter of water = One Kilogram 2.2 lb= One Kilogram(1kg) 70kg man = 154lb man (a standard reference in medicine) Think Small—Think mass One electron =9.1 x 10-31 kg One proton=one neutron=one atomic mass unit=one Dalton= 1.99x10-27 kg Think Big Mass and symbol Mass of the Earth=6x1024 kg. (circle with a cross) Mass of the Sun = 1.99x1031 kg (circle with a dot) Mass of the Universe= 1050 kg (no symbol that I know) Density Density=Mass/Volume = (the greek letter rho—looks like a p(pea) but sounds like a r. It is pronounced “row” Density of Water = 1gm/cc Density of the Sun =1.4gm/cc Density of the Earth=5.5gm/cc Scientific Notation (write the number as a word if you know it and the number in scientific notation) 10x10= one hundred 102 10x10x10= one thousand 103 1000x1000= one million 106 1000xmillion= one billion 109 1000xbillion= one trillion 1012 Write as a decimal and in scientific notation One divided by 100= .01 10-1 One divided by 1000= .001 10-3 One divided by a million=.000001 10-6 One divided by a billion= .000000001 10-9 One divided by a trillion= .000000000001 10-12 Is a negative exponent a negative number? No it is a very small number. It is an inverse not a negative number. Explain what a negative exponent means. A negative exponent signifies one divided by 10 raised to the positive exponent. So 10-2 means 1/102 or more generally 10-x=1/10x. How do you write one in SN? 100 How do you write ten in SN? 101 PREFIXES 10-1 deci101 deca 10-9 109 nanoGiga 10-2 centi102 hect- 10-12 1012 picoTera- 10-3 103 millikilo- 10-6 106 microMega 10-15 1015 femtoPeta- These distances and this velocity you should know in both miles and kilometers. Please write them Distance between Earth and Sun 93 million miles 9.3 x106 1.5 x108 km Distance of a Light Year 6 trillion miles 9.5x1012 kilometers Speed of Light 186,000 miles/sec 3x105 km/sec Speed of Sound 768 miles/hr .21miles/sec 343m/sec Finally put these wrenches in order from smallest to largest a) ¾ b) 3/16 c) 3/8 d) ½ e) 7/16 f) 9/16 B-C-E-D-F-A
