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

1.4 Area and Volume

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 = 2XX + Y = X + YX Y = XY

Area

Formulas for calculating areas for planar shapesRectangle: A = l x wTriangle: A = ½ bhCircle: A = r2

Metric AreaBasic 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. AreaFind 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 ConversionsChange 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 spaceStandard units: cm3, in3, yd3.Formulas for geometric shapes

Rectangular prism/box: V = l x w x hSphere: V = 4/3 r3

Cylinder: V = r2h

Volume

Metric volume1 liter (L) = 1 dm3 = 1000 cm3

m3 to measure large volumes1 mL = 1 cm3

Medicines and recipes measured in mL or cm3.Gasoline, in litersLarge liquid volumes in kL (1000 L)

Change 0.75 L to mL

Change 0.65 cm3 to cubic millimeter (mm3).

U.S. VolumeFind the volume of an 8 in x 5 in x 4 in box.

Change 24 ft3 to cubic inches (in3).

Metric-U.S. Volume ConversionsChange 56 in3 to cubic centimeters (cm3)

Convert 28 m3 to ft3 (1 m = 3.28 ft)

Surface AreaLateral surface areaTotal surface area