Question

What is S.I. unit of volume?
A. Cubic centimetre
B. Cubic meter
C. Cubic foot
D. Cubic millimetre

Answer 1

Hint: Convert the mathematical formula of work into basic units in the MKS system. An object having length, width and height has volume. The S.I. unit of length, width and height is meter.

Complete Step-by-Step solution:
Units used to measure different quantities vary place to place. So to have a uniformity in units a system called ‘The International System of Units’ (abbreviated as SI) is used.
There are basic seven units defines in SI system:
Length - meter (m)
Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)

The volume is the amount of space occupied by an object. Anything that has length, breadth and height has a volume. Since it is derived from length, its unit will be meter*meter*meter where meter is S.I. unit of length.

Mathematically, it is given by,
$\begin{align}
  & volume=length \times width \times height \\
 & so, \\
 & volume={{(side)}^{3}} \\
\end{align}$
Side has a unit of m or cubic meter.
This is equal to a cubic meter.
Hence the unit of volume is $m^3$ or cubic meter.
Option B. Cubic meter is correct.

Additional Information:
Other units of volume: cubic cm, litre, gallon, barrel, cubic inch etc.
The volume of regular shapes like cube, cuboid, cone, etc are calculated using algebraic formulae and volumes of irregular shapes are calculated by using integration over the space.
Volume of cube = $(side)^3$
Volume of cuboid = length*breadth*height

Note: The unit of volume will vary in a context of using it, like we are using to measure a liquid we normally use unit litre. In scientific labs the unit used for volume is cubic cm or cubic millilitre. The use of units will vary from place to place so we need to remember the interconversion formula for units from one system to another.