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Dimensions & Units

Dimensions & Units. One Dimension --- Linear Synonyms: Length Height Common English Units Mile (mi) Yard (yd) Feet (ft) Inch (in) Most Common Metric Units Meter (m) – the SI Reference Unit for length Kilometer (km) centimeter (cm) and millimeter (mm).

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Dimensions & Units

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  1. Dimensions & Units • One Dimension --- Linear • Synonyms: Length Height • Common English Units • Mile (mi) Yard (yd) Feet (ft) Inch (in) • Most Common Metric Units • Meter (m) – the SI Reference Unit for length • Kilometer (km) centimeter (cm) and millimeter (mm)

  2. Two Dimensions --- Area, Surface • Formula for a Rectangle: A = L x W • Remember to include the units with the numbers when doing our calculations • An example L = 10 ft and W = 5 ft • A = 10 ft x 5 ft = 50 ft·ft • The ft·ft means ft times ft which is ft2 • We read ft2 as “square feet” not “feet squared” although we write it that way • Other English units: mi2 in2 yd2

  3. Notice that all the examples have the superscript 2 (unit2) which indicates two dimensions • Is there a two dimensional unit in our English system that represents two dimensions but does not have the square exponent? • How about land measurement- ACRE

  4. What is the formula for a Circle • A = πr2 Note that only the radius measurement is squared • Example- radius of 5 inches • A = π(5in)2 = π (25 in·in) = π x 25 in2 The answer: A = 78.5 in2 • Please make sure that you know how to use your calculator --- you work this problem with your calculator in the same order of operation as you would solving it mathematically

  5. Metric units include square meters (m2) • Square centimeters (cm2) • Square millimeters (mm2) • Area measurements are examples of Derived Units • Derived units are those that are made up of SI Reference or Standard units that have combined

  6. Three Dimensions --- Volume • Synonyms are Capacity, and Space • Volume formulas • Block V = L x W x H • Cylinder V = π r2 h • Sphere V = 4 π r3 3 • Notice that in the Block Formula the L x W is Area (2 dimension) which we multiply by the height (1 dimension) results in three dimensions

  7. Using the Volume of a block or box as our example we have length = 15 dm width = 10 dm height = 10 dm V = L x W x H • V = 15 dm x 10 dm x 10 dm • V= 1500 dm·dm·dm which equals 1500 dm3 • Any unit of measurement that has the cubic superscript indicates volume

  8. Other cubic Metric measurements include cm3 and mm3 • Remember that we have the gallon (gal), quart (qt), pint (pt) and ounce (oz) --- they all represent three dimensional units of measurement – • Likewise the Metric system has similar units- the Liter (L), milliliters (mL)

  9. The founders of the Metric System established the cubic decimeter (1 dm3) was established as the Liter (L) • One cubic decimeter = 1 Liter by Definition • If you consider a cube that is 1 dm on each side its volume would be 1 dm3 from the formula V = 1 dm x 1 dm x 1 dm

  10. Because 1 dm = 1 cm, each side of the 1 dm3 cube becomes 10 cm x 10 cm x 10 cm • The resulting volume is 1000 cm·cm·cm which we usually write 1000 cm3 • We also know that 1 dm3 = 1 L • Using the standard prefixes we get 1 L = 1000 mL • Starting with 1 dm3 = 1 L, we get 1000 cm3 = 1000 mL, which can be reduced to 1 cm3 = 1 mL (Remember This)

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