Question

The length of each edge of a cube is 9 m. The volume of the cube in \[{{m}^{3}}\] is:
(a) 27
(b) 81
(c) 108
(d) 729

Answer 1

Hint: First of all try to recollect the shape and volume of the cube. Then, use the formula of the volume of the cube as \[{{a}^{3}}\] to find the volume of the cube where ‘a’ is the length of the edge of the cube.


Complete step-by-step answer:
We are given that the edge of a cube is 9m. We have to find the volume of the cube. Before proceeding with the question, we must know what volume is. In math, volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object. In other words, finding the volume of an object can help us to determine the amount required to fill that object like the amount of water needed to fill a bottle, an aquarium or a water tank. The volume of an object is measured in cubic units such as cubic centimeters, cubic inch, cubic foot, cubic meter, etc.

Now, the volume of a cube defines the number of the cubic units that are occupied by the cube completely. A cube is a solid three dimensional figure, which has 6 square faces or sides. To calculate the volume, we should know the dimensions of the cube.

If we know the edge length, i.e. ‘a’, then we can also find the volume of the cube. We can easily find the volume of the cube (V), by knowing the length of its edges. Suppose, the length of the edges of the cube is ‘a’. Then the V will be the product of the length, height and width. So, the volume of the cube formula is,
Volume of a cube = Length x Width x Height
In cube, Length = Width = Height = a. So, we get, Volume of cube = a x a x a
\[V={{a}^{3}}\] where ‘a’ is the length of the cube or the side of the cube or edge of the cube.

Let us consider the given cube in the question. We are given a cube of edge 9m which is as follows:

Now, we know that the volume of the cube is \[{{a}^{3}}\]. So, we get the volume of a cube of edge 9m \[={{\left( 9m \right)}^{3}}\].

\[\begin{align}
  & =9m\times 9m\times 9m \\
 & =729{{m}^{3}} \\
\end{align}\]
So, we get the volume of the cube as \[729{{m}^{3}}\].
Hence, option (d) is the right answer.

Note: Many students make the mistake of writing the unit of the volume as \[{{m}^{2}}\] which is wrong. The correct unit of the volume is cubic units that is \[{{\text{m}}^{\text{3}}}\text{, c}{{\text{m}}^{\text{3}}}\text{, }{{\left( \text{inch} \right)}^{\text{3}}}\text{, etc}\text{.}\] Also, students should keep in mind the formula of volume of a cube that is \[{{\text{a}}^{3}}\], where ‘a’ is the edge of the cube and also understand its physical significance.