Question

How do you convert a volume of $1350c{{m}^{3}}$ to cubic metres?

Answer 1

Hint: Volume is a physical quantity which measures capacity. A unit volume is used to measure the extent or the capacity of the object. The SI unit of volume is cubic metre. But the widely used metric unit of volume is in litre.

Complete step-by-step answer:Volume is defined as the amount of space occupied by the substance. Capacity is the measure of the content to hold the liquid and materials and take the shape of the container. But it is not necessary that capacity is similar to volume. It is the interior volume of the vessel.
Now, let us discuss the units of volume-
Unit of length gives the corresponding unit of volume. For example- centimetre cube is the volume of the cube having sides of one centimetre in length. But according to the international system of units, the standard unit of volume is cubic meters. The unit of volume litre also includes the metric system.
In this question, it is given that the volume is $1350c{{m}^{3}}$
$1c{{m}^{3}}$ is equal to ${{\left( {{10}^{-2}}m \right)}^{3}}$ which is equal to ${{10}^{-6}}{{m}^{3}}$
Hence, $1350c{{m}^{3}}$is equal to $1350\times {{\left( {{10}^{-2}}m \right)}^{3}}$
$1350c{{m}^{3}}$is equal to $1.35\times {{10}^{-3}}{{m}^{3}}$
Therefore, $1350c{{m}^{3}}=1.35\times {{10}^{-3}}{{m}^{3}}$

Note:We should know about cubic centimetre and cubic metre. Cubic centimetre is defined as the quantity of the cube of size one centimetre. It is denoted with the symbol $c{{m}^{3}}$ whereas cubic metre is defined as the metric unit of volume which is equal to one million cubic centimetres. It is denoted with a symbol ${{m}^{3}}$ . Students can have a lot of problems during rounding off the number. Hence a detailed knowledge is required during solving these questions.