Objectives:
• Convert area and volume units within and between measurement systems.
• Solve area and volume problems.

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

 Formulas for calculating areas for planar shapes
 Rectangle: A = l x w


Triangle: A = ½ bh
Circle: A =
 r 2

 Metric Area



Basic unit is the square meter (m 2 )
Smaller units: dm 2 , cm 2 , mm 2
Larger units: hectare (ha), km 2
 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?

 Find the smallest cross-sectional are of a 30 x 40 x
20 cm box.
 Convert 258 cm 2 to m 2 .

 U.S. Area


Find the area of a rectangle with a length of 6 in and width of 4 in.
Change 324 in 2 to yd 2 .
 Metric-U.S. Area Conversions
 Change 25 cm 2 to in 2 .
 To convert between metric and U.S. land area, use the relationship
1 hectare (ha) = 2.47 acres

 Volume – number of cubic units in a threedimensional space
 Standard units: cm 3 , in 3 , yd 3 .
 Formulas for geometric shapes



Rectangular prism/box: V = l x w x h
Sphere: V = 4/3
 r 3
Cylinder: V =
 r 2 h

 Metric volume




1 liter (L) = 1 dm 3 = 1000 cm 3 m 3 to measure large volumes
1 mL = 1 cm 3
Medicines and recipes measured in mL or cm 3 .
 Gasoline, in liters
 Large liquid volumes in kL (1000 L)
 Change 0.75 L to mL
 Change 0.65 cm 3 to cubic millimeter (mm 3 ).

 U.S. Volume
 Find the volume of an 8 in x 5 in x 4 in box.
 Change 24 ft 3 to cubic inches (in 3 ).

 Metric-U.S. Volume Conversions
 Change 56 in 3 to cubic centimeters (cm 3 )
 Convert 28 m 3 to ft 3 (1 m = 3.28 ft)
 Surface Area
 Lateral surface area
 Total surface area