Area and volume units describe how much space a shape covers or fills. A 1 unit line segment measures length in one dimension, such as meters or centimeters. When length is combined with width, it creates area measured in square units.
When length, width, and height are combined, they create volume measured in cubic units.
The powers on units show how many dimensions are being measured. A square meter, written m^2, represents a square that is 1 meter by 1 meter. A cubic meter, written m^3, represents a cube that is 1 meter by 1 meter by 1 meter.
Unit conversions must account for these dimensions, so converting area and volume requires squaring or cubing the length conversion factor.
Key Facts
- Area of a rectangle: A = l x w
- Volume of a rectangular prism: V = l x w x h
- 1 m = 100 cm, so 1 m^2 = 10,000 cm^2
- 1 m = 100 cm, so 1 m^3 = 1,000,000 cm^3
- 1 L = 1000 cm^3 and 1 mL = 1 cm^3
- To convert area, square the length conversion factor; to convert volume, cube the length conversion factor.
Vocabulary
- Length
- Length is a one-dimensional measurement of distance, such as meters, centimeters, inches, or feet.
- Area
- Area is the amount of two-dimensional surface covered by a shape, measured in square units.
- Volume
- Volume is the amount of three-dimensional space occupied by an object, measured in cubic units.
- Square unit
- A square unit is the area of a square that is 1 unit long and 1 unit wide.
- Cubic unit
- A cubic unit is the volume of a cube that is 1 unit long, 1 unit wide, and 1 unit high.
Common Mistakes to Avoid
- Converting 1 m^2 to 100 cm^2 is wrong because both dimensions must be converted, so 1 m^2 = 100 cm x 100 cm = 10,000 cm^2.
- Converting 1 m^3 to 100 cm^3 is wrong because all three dimensions must be converted, so 1 m^3 = 100 cm x 100 cm x 100 cm = 1,000,000 cm^3.
- Using linear units for area or volume is wrong because area needs square units and volume needs cubic units to show the number of dimensions measured.
- Multiplying only two dimensions for volume is wrong because volume of a rectangular prism requires length, width, and height.
Practice Questions
- 1 A rectangle is 8 cm long and 5 cm wide. What is its area in cm^2?
- 2 A rectangular prism is 4 m long, 3 m wide, and 2 m high. What is its volume in m^3, and what is that volume in cm^3?
- 3 Explain why 1 m^2 is not equal to 100 cm^2 even though 1 m is equal to 100 cm.