8.02 Length, Area and Volume

Page 1: Introduction to Length, Area, and Volume

Examples of length measurements with the appropriate metric unit:
- a) Height of the Ted Williams statue – meters
- b) Length of your arm – centimeters
- c) Length of a flea – millimeters
- d) Height of the Sears Tower in Chicago – meters
- e) Diameter of a half-dollar – centimeters
- f) Distance between Amarillo, Texas, and Detroit, Michigan – kilometers
- g) Diameter of a round wastepaper basket – centimeters
- h) Diameter of a pencil – centimeters
- i) Your waist size – centimeters
- j) Your height – meters

Examples of area measurements with the appropriate metric unit:
- a) Yellowstone National Park – square kilometers
- b) The top of a kitchen table – square meters
- c) The floor of the classroom – square meters
- d) A person's property with an average-sized lot – square meters
- e) A newspaper page – square decimeters
- f) A baseball field – acres or square meters
- g) An ice-skating rink – square meters
- h) A dime – square centimeters
- i) A lens in eyeglasses – square centimeters
- j) A dollar bill – square centimeters

Conversion: 1 m² = 10,000 cm²
A square meter is 10,000 times larger than a square centimeter.
- Illustration of conversion process:
  - 1 m = 100 cm
  - 1 m² = 100 cm x 100 cm = 10,000 cm²

Example: Calculate the area of a table top with:
- Length = 1.5 m
- Width = 1.1 m
Area Calculation: Area = Length x Width = 1.5 m x 1.1 m = 1.65 m²

Example: A quarter has a diameter of about 2.4 cm.
Surface Area Calculation:
- Use formula for surface area of a circle: A = πr² where r = diameter/2
- Surface Area = π(1.2 cm)²

Examples of volume measurements with the appropriate metric unit:
- a) Water in a swimming pool – kiloliters
- b) A carton of milk – liters
- c) Truckload of topsoil – cubic meters
- d) A drug dosage – milliliters
- e) Sand in a paper cup – cubic centimeters
- f) A dime – cubic centimeters
- g) Water in a drinking glass – milliliters
- h) Water in a full bath tub – liters
- i) Storage area of an SUV – cubic meters
- j) Concrete for a foundation – cubic meters

Example: For a pool with dimensions:
- Length = 18 m
- Width = 9 m
- Depth = 3 m
Volume Calculation:
- Volume = Length x Width x Depth = 18 m x 9 m x 3 m = 486 m³
- Convert to kiloliters (1 m³ = 1 kL): Volume = 486 kL

Volume Measurement Abbreviations:
- cc = cm³
- Example: Nurse administering drugs:
  - a) Drug dosage: 3 cc (or 3 mL)
  - b) Total volume with saline: Drug (3 cc) + Saline (100 cc) = 103 cc = 103 mL

Example: Right circular cylinder hot-water heater
- Radius = 50 cm, Height = 148 cm
Capacity Calculation in liters:
- Volume = πr²h
- Convert cm³ to liters (1 L = 1000 cm³)

Volume Comparison Questions:
- a) How many times larger is a cubic meter than a cubic centimeter?
- b) How many times larger is a cubic dekameter than a cubic meter?