Question

How do you find the volume of a cube with edge length of $11$?

Answer 1

Hint: In the problem they have given the edge length of a cube which is a three-dimensional object. We know that for three dimensional objects we have several parameters like surface area, curved surface area, volume based on the shape of the three-dimensional object. In this problem they have asked to calculate the volume of a cube. We know that the volume of the cube having side length $a$ will be given by $V={{a}^{3}}$. From this formula we can easily calculate the volume of the cube having the edge length $11$.

Complete step by step answer:
Given that,
The edge length of the cube is $11$.
We know that the volume of a cube which is having the edge length $a$ will be $V={{a}^{3}}$.

Now the volume of the cube which is having the edge length $11$ is given by
$V={{11}^{3}}$
We can write ${{a}^{n}}=a.a.a.a.a.a....\text{ n times}$. Based on this rule we can write the volume of the cube as
$V=11\times 11\times 11$
We know that the value of $11\times 11=121$, substituting this value in the above equation, then we will get
$V=121\times 11$
We know that the value of $121\times 11=1331$, substituting this value in the above equation, then we will get
$V=1331$ cubic units.

Note:
As we discussed above the three-dimensional shapes have different parameters. When it comes to the cube, the cube has three parameters which are Volume, Surface area, Space Diagonal. In this problem they have only asked volume, if they have asked to calculate the remaining parameters, then we can use the below formulas to get the result.
Surface area of the cube having edge length $a$ is $A=6{{a}^{2}}$ square units.
Space diagonal length of the cube having the edge length $a$ is $S=\sqrt{3}a$ units.