Question

Prove that 1000 cm³ = 1 L
Prove that 1 m³ = 1000 L

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Answer 1

Answer:

Several comments refer to the liter as “formerly” 1 kg of water at 4 °C. Actually, the original French definition was 1 cubic decimeter. From 1904 to 1964, a mere 60 years of its 223 year life, it was defined as exactly 1 kg H2O at 4 °C. That decision was abrogated in 1964.

Howard is right about the comma in “1,000” but I know 1 L = 1000 cm³, “cause the SI Brochure tells me so.” Quote follows (from Table 6 in Section 4)

1 L = 1 l = 1 dm³ = 10³ cm³ = 10^−3 m³

This expresses very succinctly that either capital or lowercase L may be used as the symbol and it is equal to 1 cubic decimeter, 1000 cubic centimeters or one-thousandth of a cubic meter. Since the SI Brochure defines the SI and declares equality, it can’t be unequal, by definition.

Answer 2

Take a cubical container of side 10 cm

Fill this with full of water

Now you will be find that this will contain 1 L

So Volume = 1L = (10 cm) ^3

Similarly you can prove that 1m^3 = 1000L