1.3 Volume

Volume

1.3 Volume

  • Definition of Volume:

    • Volume is defined as a three-dimensional measurement (length, width, height) of the space occupied by an object or a substance.

  • Illustration of Volume Change:

    • Example with a balloon being blown up, indicating that as air is added, the volume increases.

1.3.1 What is Volume?

  • Comparison of a cellphone and a wallet:

    • Despite having different shapes and dimensions, both can have similar volumes.

  • Key Concept:

    • Objects that appear different can occupy the same amount of space (i.e., have the same volume).

    • Objects with the same mass can possess different volumes.

  • Example:

    • A cellphone has a volume of 80 cm³, while a wallet also has a volume of 80 cm³.

    • Three objects (brass, water, light wood) all have different volumes but can share the same mass of 10 g (measured without their containers).

1.3.2 Which Units of Measurement Do We Use for Volume?

  • Measurement Units:

    • Depending on the object or substance, units can vary; often measured in litres or cubic metres.

  • Base Unit:

    • The cubic metre (m³) is the base unit for volume measurement.

    • Litres and multiples are often used for liquids and gases.

  • Conversions:

    • Note that 1 L equals 1000 cm³ and 1 ml equals 1 cm³.

Units of Measurement for Volume (Cubic Measurements)

Name

Value

Symbol

cubic kilometre

10^9 m^3 or 1,000,000,000 m^3

km³

cubic hectometre

10^6 m^3 or 1,000,000 m^3

hm³

cubic decametre

10^3 m^3 or 1,000 m^3

dam³

cubic metre

1 m^3

m³

cubic decimetre

$10^{-3} m^3 or 0.001 m^3

dm³

cubic centimetre

$10^{-6} m^3 or 0.000001 m^3

cm³

cubic millimetre

$10^{-9} m^3 or 0.000000001 m^3

mm³

cubic micrometre

$10^{-18} m^3

μm³

  • Most-used units are highlighted in bold.

    • Multiplicative Relationships:

  • Transitioning between the units often requires multiplication or division by 1000.

Units of Measurement for Volume (Multiples of Litres)

Name

Value

Symbol

kilolitre

1000 L

kl

hectolitre

100 L

hl

decalitre

10 L

dal

litre

1 L

L

decilitre

10^{-1} L or 0.1 L

dl

centilitre

10^{-2} L or 0.01 L

cl

millilitre

10^{-3} L or 0.001 L

ml

microlitre

10^{-6} L or 0.000001 L

μl

  • Most-used units are highlighted in bold.

The Volume of Water

  • Understanding Volume Sizes:

    • Some examples of different volumes of water:

    • All water on Earth: Approximately 1,400,000,000,000,000,000,000 L (or 1400 million km³).

    • Contents of a bathtub: Approximately 150 L.

    • Contents of a washing machine: 60 L.

    • Contents of a glass of water: 200 ml.

    • A drop of water: 0.05 ml.

  • Measurement Considerations:

    • The choice of volume unit should avoid excessively large or small numerical representations.

One Way to Measure the Volume of a Liquid

Required Tools and Steps:

  1. Use a Graduated Cylinder:

    • This is the most precise instrument for measuring liquids.

  2. Observe Graduating Marks:

    • Look at the smallest division on the graduated cylinder to determine measurement increments.

  3. Pour the Liquid:

    • Add the liquid whose volume you wish to measure into the graduated cylinder.

  4. Read the Volume:

    • Determine the liquid level using the lowest point of the meniscus (the curvature of the liquid surface) for an accurate read; for example, if the meniscus level is at the last line before 15 ml, the volume is 14.5 ml.

How to Measure the Volume of a Solid

  • Methodology:

If the Solid Has a Regular Shape:

  • Use mathematical formulas:

    • For a cube:
      V=L\cdot W\cdot H
      where L = length, W = width, and H = height.

If the Solid Has an Irregular Shape:

  • Use the graduated cylinder method or an overflow vessel:

Measurement Method Using a Graduated Cylinder:

  1. Fill the graduated cylinder with water and record the volume.

  2. Immerse the solid into the cylinder, then record the new volume.

  3. Calculate the volume of the solid by finding the difference between the two volumes recorded.

Measurement Method Using an Overflow Vessel:

  1. Fill the overflow vessel until the spout height is achieved.

  2. Place a graduated cylinder or beaker to catch overflow water.

  3. Insert the solid into the overflow vessel.

  4. Measure the volume of water displaced into the graduated cylinder or beaker, which equals the volume of the solid.

    • Addition of a solid will cause a rise in the water level in the graduated cylinder; this difference represents the solid's volume.

Activities

  1. Reading Liquid Volume:

    • Make sure to account for the curve of the liquid’s surface.

    • a) Identify the proper angle for reading the measurement.

    • b) Remember the curve is called the "meniscus."

  2. Volume Unit Selection:

    • Select the most appropriate unit of measurement:

    • a) A pencil takes up (20 cm³ or 20 ml).

    • b) A can holds (1 L or 355 ml).

    • c) A backpack can hold (1 m³ or 30 L).

    • d) A cubby has a volume of (0.39 m³ or 2 m³).

    • e) Lungs can hold around (3.5 L or 1 m³).

  3. Cylinder Liquid Measurements:

    • Indicate liquid levels in various graduated cylinders shown in diagrams.

  4. Measurement Unit Selection for Various Objects:

    • a) The Sun.

    • b) A bowl of soup.

    • c) A fly.

    • d) A gas tank.

    • e) A soccer ball.

    • f) A dose of a vaccine.

  5. Volume Determination Method:

    • a) For a rock of about 5 cm in diameter.

    • b) A marble of about 1 cm in diameter.

    • c) A wooden cube.

  6. Mass Comparison:

    • a) Explain which is easier to move: a box of 1 kg of feathers or 1 kg of iron.

    • b) Discuss the ease of moving a box of 1 L of feathers versus 1 L of iron.