Metric Volume & Capacity

Statement

In the metric system, volume and capacity are directly linked:

\[ 1 \text{ cm}^3 = 1 \text{ mL}, \quad 1000 \text{ cm}^3 = 1 \text{ L} \]

Why it’s true

• The metric system is designed so that units of volume and capacity match up neatly.
• A cube measuring 1 cm × 1 cm × 1 cm has a volume of 1 cm³, which is defined as exactly 1 millilitre (mL).
• Since 1000 millilitres = 1 litre, a volume of 1000 cm³ = 1 L.

Recipe (how to use it)

1. To convert cm³ to mL: use 1 cm³ = 1 mL.
2. To convert cm³ to litres: divide by 1000.
3. To convert litres to cm³: multiply by 1000.

Spotting it

Whenever you are given a volume in cm³ (like from a geometry calculation), you can quickly convert it to a liquid capacity in mL or L.

Common pairings

• Geometry problems (cuboids, cylinders, spheres) where the answer is in cm³ but needs to be expressed in litres or mL.
• Real-life contexts such as water tanks, bottles, or measuring containers.

Mini examples

1. A cube with side 5 cm has volume 5³ = 125 cm³. Capacity: 125 mL.
2. A tank has volume 2500 cm³. Capacity: 2500/1000 = 2.5 L.

Pitfalls

• Forgetting the link: cm³ and mL are interchangeable (1-to-1).
• Mixing units: Don’t confuse cm³ with m³ (1 m³ = 1000 L, not 1 L).
• Arithmetic slips: Watch out when dividing or multiplying by 1000.

Exam strategy

• Always write down whether the question wants volume (cm³) or capacity (mL/L).
• Do the geometry calculation first in cm³, then convert if needed.
• Check: litres are bigger units, so the number should get smaller when converting cm³ → L.

Summary

Key facts: 1 cm³ = 1 mL, and 1000 cm³ = 1 L. Use these to switch between solid volumes and liquid capacities in problems.