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

2. 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

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

4. 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?

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

6. 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

7. 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  r 3 Cylinder: V =  r 2 h

8. 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 ).

9. 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 ).

10. 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