# 1.4 Area and Volume 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 three dimensional 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  Cylinder: V = 

r

2

h r

3

 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