Handy conversion: 1 cubic metre (1 m^3) is approximately equal to how many litres or cubic feet?

Introduction / Context:Unit conversions between SI and Imperial systems are routine in design, data sheets, and vendor specifications. Remembering a few anchor conversions improves accuracy and speed. One such anchor is the relation between cubic metres, litres, and cubic feet, used in tank sizing, ventilation, and gas metering.

Given Data / Assumptions:

• 1 m = 100 cm; 1 L = 1 dm^3 = 0.001 m^3.
• 1 m^3 = 1000 L exactly (by definition).
• 1 ft = 0.3048 m exactly, hence 1 m^3 = (1 / 0.3048)^3 ft^3 ≈ 35.3147 ft^3.

Concept / Approach:Use exact definitions for base units to compute derived volume conversions. When selecting from approximate multiple-choice options, choose the closest value to the exact conversion while rejecting clearly incorrect litre values that differ by orders of magnitude.

Step-by-Step Solution:

Verification / Alternative check:Reverse check: 35 ft^3 * (0.0283168 m^3/ft^3) ≈ 0.991 m^3, close to 1 m^3; the small difference is due to rounding of “35”.

Why Other Options Are Wrong:

• 28 L and 4.5 L: off by a factor of ~36 and ~222 respectively; 1 m^3 is much larger (1000 L).
• 4.5 ft^3: too small; about one-eighth of a cubic metre is ~4.3 ft^3, not 1 m^3.
• 100 L: still an order of magnitude too small.

Common Pitfalls:Confusing litres with cubic decimetres; mixing length and volume conversions; misremembering 1 ft = 0.3 m without squaring/cubing when moving to area/volume.

Final Answer:35 ft^3