Question

Which one of the following is equal to exactly one cubic meter (1 m^3)? Why?

A. 10^8 cm^3

B. 10^2 L

C. 10^10 mm^3

D. 10^6 mL

Answer 1

A) 10^8 cm^3

1m=100cm

1cm=1/100m=10^-2 m

So 1cm^3=(10^-2 m)^3=10^-6 m^3

Which gives 10^8 cm^3=10^8 *10^-6 m^3=10^2 m^3 (not equal to 1m^3)

B) 1L=1dm3

1m=10dm

1dm=10^-1m

1dm^3=(10^-1m)^3=10^-3 m^3

So 1L=10^-3 m^3

Which gives 10^2 L=10^2 *10^-3 m^3 =10^-1 m^3 (not equal to 1m3)

C)1m=1000mm

So 1mm=10^-3 m

1mm^3=(10^-3 m)^3=10^-9 m^3

Which gives 10^10 mm^3=10^10 *10^-9 m^3=10 m^3(not equal to 1m3)

D)1ml=1cm3

1cm=10^-2m

1cm^3=(10^-2m)^3=10^-6 m^3

So 1ml=10^-6 m^3

Which gives 10^6 ml=10^6 *10^-6 m^3=1 m^3 (right option)