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Question: > What should be the volume of the milk \((inm^{3})\) which measures 5 L? > >...

What should be the volume of the milk (inm3)(inm^{3}) which measures 5 L?

A

5×10−3m35 \times 10^{- 3}m^{3}

B

5×103m35 \times 10^{3}m^{3}

C

5×10000m35 \times 10000m^{3}

D

5×106m35 \times 10^{6}m^{3}

Answer

5×10−3m35 \times 10^{- 3}m^{3}

Explanation

Solution

(1) : Since 1 L = 1000 cm3cm^{3}

and 1 m = 100 cm

1m100cm=1=100cm1m,\frac{1m}{100cm} = 1 = \frac{100cm}{1m}, or

(1m100m)3=1m3106cm3=13=1\left( \frac{1m}{100m} \right)^{3} = \frac{1m^{3}}{10^{6}cm^{3}} = 1^{3} = 1

Hence , 5 L = 5×1000cm3×1m3106cm3=5m3103cm^{3} \times \frac{1m^{3}}{10^{6}cm^{3}} = \frac{5m^{3}}{10^{3}}= 5×10−3m35 \times 10^{- 3}m^{3}