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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 *= 2*X* *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