Question

How many cubic centimetres ${cm^3}$ are in a cubic metre ${m^3}$?
A. ${10^3}$
B. ${10^6}$
C. ${10^9}$
D. ${10^{12}}$

Answer 1

Hint: Units and Dimensions play key roles in physics. Various quantities have various dimensions. Dimensions of the main fundamental quantities are M for mass while L for length T for time K for temperature while A for the current. Different physical quantities have various units and the SI unit of length is meter.

Formula used:
$1m = 100cm = {10^2}cm$

Complete step by step answer:
It's known that there are various languages in this world. Same feelings are expressed in different languages using different terms. But when we measure a certain quantity of a body let it be mass or length or volume it remains constant wherever we go in this world. Hence scientists had thought that there should be common units to measure these quantities which will be acceptable and understood all over the world without any difficulties. Those units are called SI units or international systems of units. Meter is the SI unit of the length. For mass its kilogram and for time its second.
Now there is another system of units. This is called the CGS system. Here mass is measured in grams and length is measured in centimeters and time is measured in seconds.
Generally to measure length in daily life we will be using a meter scale which has the least count of 0.001m.
We have
$\eqalign{
  & 1nm = {10^{ - 9}}m \cr
  & 1mm = {10^{ - 3}}m \cr
  & 1\mu m = {10^{ - 6}}m \cr} $
$1{m^2}$ is the unit for the area while $1{m^3}$ is the unit for the volume
$\eqalign{
  & 1m = 100cm \cr
  & 1{m^2} = 100 \times 100c{m^2} \cr
  & 1{m^3} = 100 \times 100 \times 100c{m^3} \cr
  & 1{m^3} = {10^6}c{m^3} \cr} $

So, the correct answer is “Option B”.

Note:
There are some quantities which have units while don't have dimensions. Few instances for that are plane angle which has unit or radian but no dimensions and solid angle which has a unit of steradian and no dimension and angular displacement also has unit of radian but no dimension.