Volume and Capacity

Volume vs. Capacity

• Volume denotes the three-dimensional space occupied by an object.
• Area is two-dimensional, length is one-dimensional, and volume is three-dimensional.
• Capacity refers to the potential volume that a container can hold, often for liquids or gases.
• Capacity is commonly measured in liters, while volume is often measured in cubic meters.

Volume of a Rectangular Prism

• The volume of a rectangular prism is found by multiplying its length, width, and height: Volume = Length × Width × Height.
• Multiplying length and width determines the area of the base, then multiplied by the height to calculate the third dimension.
• The dimensions include length (distance), then length × width (area), and finally height to establish the volume.

Volume of a Cube

• A cube has equal sides so the volume of a cube is calculated by cubing the length of one of its sides (Length³).

Cubic Units Conversion

• All three dimensions (not just one) affect the conversion factor when converting cubic units.
• To convert cubic kilometers to cubic meters, multiply by 1,000 cubed (1,000 * 1,000 * 1,000).
• To convert meters to centimeters, multiply by 100 cubed (100 * 100 * 100), because 1 meter contains 100cm.
• To convert centimeters to millimeters, multiply by 10 cubed (10 * 10 * 10), because 1cm contains 10mm.
• Conversely, division by these factors is required to convert to smaller units.

Liters Unit Conversion

• One megaliter (ML) equals 1 million liters.
• One kiloliter (kL) equals 1,000 liters.
• One milliliter (mL) equals 1/1000th of a liter.
• Conversion between liter units involves multiplying or dividing by 1,000, depending on the units.

Cubic Meters and Liters

• 1 cubic centimeter (1 cm³) is equivalent to 1 milliliter (1 mL).
• 1 cubic meter (1 m³) is equivalent to 1,000 liters.
• A cubic meter, measuring 1 m by 1 m by 1 m, can hold a substantial amount of 1,000 liters.

Examples

• A rectangular prism with length 4m, width 6m, and height 2m has a volume of 6 * 4 * 2 = 48 m³.
• The order in which the length or width is provided does not matter.
• A rectangular prism measuring 20cm long, 10cm wide, and 15cm high has a capacity of 20 * 10 * 15 = 3,000 cm³, which equals 3,000mL.
• 3,000mL divided by 1,000 equals 3 Liters.