9.2 Measuring Area and Volume

Area• Area is measured in square units

• Area can be found be counting the number of square units

1 unit

1 unit

A = 1 square unit

A = 12 square units

Square units of measure

• 1 square foot (ft2) = 144 square inches (in2)

• 1 square yard (yd2) = 9 square feet (ft2)

• 1 acre (a) = 43,560 square feet (ft2) or 4,840 square yard (yd2)

• 1 square mile (mi2) = 640 acres

Population density

• Population density is the population of a region divided by the area of the region

population density =

Example: The population of Berkeley, CA is 103,000 and its area is 5.1 (mi2). What is the population density?

population

area

Example: find the population density

• The population of Alaska is 494,423 and the area is 97,818 (mi2).

English/metric equivalents

• A hectare is the metric equivalent of an acre. It is approximately 2 football fields side by side.

• 1 acre = 0.4 hectare (ha)

• Example: A property in Italy sells for $545,000 for 6.8 hectares. What is the price per acre?

Volume

• Volume is measure in cubic units

• 1 cubic yard =27 cubic feet

• 1 cubic foot = 1728 cubic inches

1 unit 1 unit 1 unit

1 cubic unit

V l w h

Capacity

• Capacity is the amount of fluid a 3D object can hold

• 2 pints (pts)= 1 quart(qts)

• 4 quarts = 1 gallon (gal)

• 1 gallon = 128 ounces (oz)

• 1 cup = 8 ounces

Volume and capacity

• 1 cubic yard = 200 gal (approximate)

• 1 cubic feet = 7.48 gal

• 231 cubic inches = 1 gal

Example

• A swimming pool has a volume of 22,500 cubic feet. How many gallons of water can it hold?

• A water tank has a volume of 8 cubic yards. How many gallons of water can it hold?

Metric Capacity

• The basic metric unit is the liter (L)

1 liter = 1.0567 quarts

Volume = Metric Capacity

1 cm3 = 1 mL

1000 cm3 = 1 L

1 m3 = 1 kL

1 dm3 =1 L

Example

• An aquarium holds 36,000 cm3. How many liters does it hold?

Hw: p. 477/1-36,45-48