Question

The volume of a cubical box is 21952 ${{m}^{3}}.$ Find the length of the side of the box.

Answer 1

Hint: We solve this question by using the basic concepts of volume of standard figures. Here, we are given the volume of a cubical box or a cube. We need to calculate the side of the box which can be done by using the formula for the volume of a cube. The volume of the cube is given by $V={{s}^{3}}\text{ }{{m}^{3}}.$ Here, s is the length of one side of the cube and ${{m}^{3}}$ or $metr{{e}^{3}}$ is the units for the volume. Using the value of volume in this formula and taking the cube root of this value, we obtain the side of the cube.

Complete step-by-step solution:
In order to answer this question, let us specify the volume of a cube or cubical box. A cube is a three-dimensional figure having equal dimensions on all 3 sides, that is, having the same length, breadth and height. Its volume is calculated by taking a product of all the three sides. Let us assume one side of the cube is given by s. This is shown in the figure below,

Then the volume of the cube is given as,
$\Rightarrow Volume=s\times s\times s={{s}^{3}}$
It is measured in cubic units such as ${{m}^{3}},$ $c{{m}^{3}},$ etc.
Now, in order to calculate the length of the side of a cube whose volume is given, we need to substitute the value of the volume in the above formula and simplify for the side. Given volume is 21952 ${{m}^{3}}.$ Using this in the above formula,
$\Rightarrow 21952={{s}^{3}}$
Taking cube root in both sides,
$\Rightarrow \sqrt[3]{21952}=\sqrt[3]{{{s}^{3}}}$
The term on the right-hand side becomes s and the cube root of 21952 is found out to be,
$\Rightarrow 28=s$
Hence, the length of the side of the box is found out to be 28 m.

Note: We need to know the basic formula for calculating volume of standard figures to solve such problems. It is important to note that the units for volume is considered in terms of cubic units such as $metr{{e}^{3}}$ , $centimetr{{e}^{3}}$ , etc.