A tumbler contains 3 L of water Calculate the volume of the water in `m^(3)`.

Explanation

We know that, 1 m-100 cm and `1 L - 10^(3)cm^(3)`
To get `m^(3), 1 m^(3)=(100 cm)^(3)=10^(6)cm^(3)`
As, `1 L = 10^(3) cm^(3)`
`therefore 1 m^(3)=(10^(6)cm^(3))/(10^(3) cm^(3))=10^(3) L`
Hence, `1 L=10^(-3) m^(3)`
`therefore 3 L` of water `= 3xx10^(-3)m^(3)`
OR
Since, `1 L = 1000 cm^(3)` and 1 m = 100 cm which gives
`(1 m)/(100 cm) = 1 = (100 cm)/(1 m)`
To get `m^(3)` from the above unit factors, the first unit factor is taken and it is cubed.
`((1 m)/(100 cm))^(3) rArr (1 m^(3))/(10^(6)cm^(3))=(1)^(3)=1`
Now, `3 L = 3xx1000 cm^(3)`
The above is multiplied by the unit factor.
`3xx1000 cm^(3)xx(1m^(3))/(10^(6)cm^(3))=(3 m^(3))/(10^(3))=3xx10^(-3)m^(3)`.