Question

If one liter of water to fill in a cube shaped tin, what are the measurements required of the cube (in cms) ? Explain.

Answer 1

Hint: In the problem they have mentioned that one liter of water is filled in a cube i.e. here we have the volume of the cube as one liter. Now we will assume the dimensions of the cube as $x$ cm. Now we will calculate the volume of the cube by using the formula $V={{a}^{3}}$, where $a$ is the side length of the cube. After calculating the volume of the cube, we will equate the calculated volume to the given volume of the cube to find the value of side length of the cube. Here the calculated volume and the given volume of the cube are in different units, so we need to do unit conversion between liters and $ c{{m}^{3}}$ by using the known relation $1lit=1000c{{m}^{3}}$.

Complete step by step answer:
Given that, one liter of water is filled in the cube. We know that the space inside the solid to occupy is known as the volume of the solid. So, the volume of the cube is given by
$V=1lit$
Let the side length of the cube is $x$ cm as shown in below figure.

Now the volume of the above cube is given by
$V={{x}^{3}}c{{m}^{3}}$
According to the problem the volume is $V=1lit$.
$\therefore {{x}^{3}}c{{m}^{3}}=1lit$.
We have the relation between $ c{{m}^{3}}$ and liters as $1lit=1000c{{m}^{3}}$.
$\therefore {{x}^{3}}c{{m}^{3}}=1000c{{m}^{3}}$
Taking cube root on both sides of the above equation, then we will get
$x=10cm$

$\therefore $The measurement of the cube is $10$ cm.

Note: In the problem they asked to calculate the measurement in centimeters, so we have assumed the side length of the cube in centimeters and used the relation between $ c{{m}^{3}}$ and liter. If they have asked to calculate the measurement of the cube in meters, then we need to assume the side length in meters and calculate the volume in ${{m}^{3}}$. Then we need to use the relation between ${{m}^{3}}$ and liter which is $1{{m}^{3}}=1000lit$ and solve the problem.