Question

Choose the correct option from the following;
$1000l = ?$

A.)$1ml$
B.)$1{m^3}$
C.)$1c{m^2}$
D.)$1000{m^3}$

Answer 1

Hint- Here we will need a conversion factor. For that we will proceed with writing the conversion as a fraction that equals one, then multiplying it and also leaving all units in the answer, then finally cancel out the units which are in both denominator and numerator.

Step By Step Answer:
As we all know that the 1 litre is equal to the 1000 cc that is 1000 cubic centimetre. So now we will write this in a mathematical form as follows,

$1l = 1000cc$
$1l = 1000$$c{m^3}$-----equation (1)

Also, we know that in \[1m\] there are $100cm$ and with the help of this conversion we also have 1 centimetre is equal to the ${10^{ - 2}}$ metre.

We can write this as,

$1cm = \dfrac{1}{{100}}m$

Now we will put this value of the $1cm$ in the equation (1), then we get

$1l = 1000 \times {\left( {\dfrac{1}{{100}}m} \right)^3}$
Now we will get the value of $1l$ in metres as follows,
$1l = 1000 \times \dfrac{1}{{1000000}}{m^3}$
$1l = \dfrac{1}{{1000}}{m^3}$

So now I have got the value of the $1l$ as $\dfrac{1}{{1000}}{m^3}$.

Hence we have $1l = 0.001{m^3}$.

Now we can calculate the value of the $1000l$ as follows,

Since $1l = 0.001{m^3}$
So, $1000l = 1{m^3}$

Hence the option (B) is the correct answer.

Note- Cubic metre written as ${m^3}$ is the SI unit of the volume. It is the volume of a cube having $1m$ length, $1m$ breadth and $1m$ height. Here due to the mention of the two units we should have the proper idea of its actual application. Litre $(l)$ is used to measure the capacity and volume is measured in ${m^3}$. Capacity is an amount of space inside a solid that can be filled and volume is the amount of the space that a solid can occupy. Let us take an example-
A box has both volume and capacity while a stone is having volume but this stone doesn’t have capacity. So, we can say that only hollow bodies can have capacity.