Question

The ratio of the CGS unit of volume to that of the SI unit of volume is $1:{10^6}$.
(A) True
(B) False

Answer 1

Hint The CGS system and the SI system are two different systems that use different units for calculation. In the CGS system, we take lengths in centimeters, mass in grams, and time in seconds. In the SI system, we take the length in meters, mass in kilograms, and time in seconds.

Complete Step by step solution
In the CGS system, we take the length in centimeters.
We know that volume can be written as,
${V_{CGS}} = {l^3}$
If we take $l = 1cm$ then
${V_{CGS}} = {1^3} = 1c{m^3}$
In the SI system, the length is taken in meters
i.e.
$l = 1m$
$ \Rightarrow l = 100cm$
The volume will be
${V_{SI}} = {l^3} = {100^3} = {10^6}c{m^3}$
The ratio will be,
${V_{CGS}}:{V_{SI}} = 1:{10^6}$
Therefore the statement is true.

The answer is: Option (A): True.

Additional Information
There are different systems for units that are the F.P.S system in which we use foot for length, pound for mass, and second for time. Next is the C.G.S system which we have already mentioned. The next is the M.K.S system where we take the length in meters, mass in kilograms, and time in seconds. The S.I system of units is the modified form of the M.K.S system. The internationally accepted system of units for measurements is the Systeme Internationale d'Unites (the French word for International system of units) and abbreviated as S.I. This system of units was developed and recommended by the ‘General conference on weights and measures’ in 1971.

Note
Here we converted the lengths into units of centimeters and calculated the volume. Then we took the ratio of the volumes. In another way, we can first find the volumes in both systems respectively, and convert it into centimeters to get the same answer.