objectives: convert area and volume units within and between measurement systems. convert area and...
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Objectives:•Convert area and volume units within and between measurement systems.•Solve area and volume problems.
1.4 Area and Volume
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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 = 2XX + Y = X + YX Y = XY
Area
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Formulas for calculating areas for planar shapesRectangle: A = l x wTriangle: A = ½ bhCircle: A = r2
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Metric AreaBasic 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?
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Find the smallest cross-sectional are of a 30 x 40 x 20 cm box.
Convert 258 cm2 to m2.
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U.S. AreaFind 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 ConversionsChange 25 cm2 to in2.
To convert between metric and U.S. land area, use the relationship
1 hectare (ha) = 2.47 acres
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Volume – number of cubic units in a three-dimensional spaceStandard units: cm3, in3, yd3.Formulas for geometric shapes
Rectangular prism/box: V = l x w x hSphere: V = 4/3 r3
Cylinder: V = r2h
Volume
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Metric volume1 liter (L) = 1 dm3 = 1000 cm3
m3 to measure large volumes1 mL = 1 cm3
Medicines and recipes measured in mL or cm3.Gasoline, in litersLarge liquid volumes in kL (1000 L)
Change 0.75 L to mL
Change 0.65 cm3 to cubic millimeter (mm3).
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U.S. VolumeFind the volume of an 8 in x 5 in x 4 in box.
Change 24 ft3 to cubic inches (in3).
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Metric-U.S. Volume ConversionsChange 56 in3 to cubic centimeters (cm3)
Convert 28 m3 to ft3 (1 m = 3.28 ft)
Surface AreaLateral surface areaTotal surface area