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1.4 Area and Volume

1.4 Area and Volume. Objectives: Convert area and volume units within and between measurement systems. Solve area and volume problems. Area. Area – number of square units in a two-dimensional space. When calculating with unit quantities, treat the units as factors in algebra.

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1.4 Area and Volume

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  1. 1.4 Area and Volume Objectives: Convert area and volume units within and between measurement systems. Solve area and volume problems.

  2. Area • Area – number of square units in a two-dimensional space. • When calculating with unit quantities, treat the units as factors in algebra. X X = X2 X + X = 2X X + Y = X + Y X Y = XY

  3. Formulas for calculating areas for planar shapes • Rectangle: A = l x w • Triangle: A = ½ bh • Circle: A =  r2

  4. Metric Area • Basic unit is the square meter (m2) • Smaller units: dm2, cm2, mm2 • Larger units: hectare (ha), km2 • Find area of a 5 x 3 meter rectangle • A 10 by 8 centimeter metal plate has a 6 by 4 centimeter rectangular piece cut out from the center. What is the area of the metal plate after the piece was removed?

  5. Find the smallest cross-sectional are of a 30 x 40 x 20 cm box. • Convert 258 cm2 to m2.

  6. U.S. Area • Find the area of a rectangle with a length of 6 in and width of 4 in. • Change 324 in2 to yd2. • Metric-U.S. Area Conversions • Change 25 cm2 to in2. • To convert between metric and U.S. land area, use the relationship 1 hectare (ha) = 2.47 acres

  7. Volume • Volume – number of cubic units in a three-dimensional space • Standard units: cm3, in3, yd3. • Formulas for geometric shapes • Rectangular prism/box: V = l x w x h • Sphere: V = 4/3  r3 • Cylinder: V =  r2h

  8. Metric volume • 1 liter (L) = 1 dm3 = 1000 cm3 • m3 to measure large volumes • 1 mL = 1 cm3 • Medicines and recipes measured in mL or cm3. • Gasoline, in liters • Large liquid volumes in kL (1000 L) • Change 0.75 L to mL • Change 0.65 cm3 to cubic millimeter (mm3).

  9. U.S. Volume • Find the volume of an 8 in x 5 in x 4 in box. • Change 24 ft3 to cubic inches (in3).

  10. Metric-U.S. Volume Conversions • Change 56 in3 to cubic centimeters (cm3) • Convert 28 m3 to ft3 (1 m = 3.28 ft) • Surface Area • Lateral surface area • Total surface area

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