Transcript 1.4 Area and Volume - Zamora's Science Zone

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 = X2
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 =  r2
 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?
 Find the smallest cross-sectional are of a 30 x 40 x
20 cm box.
 Convert 258 cm2 to m2.
 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
 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
 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).
 U.S. Volume
 Find the volume of an 8 in x 5 in x 4 in box.
 Change 24 ft3 to cubic inches (in3).
 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