Question

If the volume of a cube is \[512c{m^3}\] , then what is the length of each edge in \[cm\] ?

Answer 1

Hint: According to the question, first we need to figure out what we have to find out. Then we will try the formula of the volume of a cube. We will put the values given in the question, and try solving it.

Complete step-by-step answer:
The question is that we are having a cube. The volume of the cube is given which is \[512\;c{m^3}\] . We have to calculate the length of the edge. We know that the formula for the volume of the cube with side ${\text{a}}$ is

Volume of the cube \[ = {\text{a}} \times {\text{a}} \times {\text{a}} = {({\text{a}})^3}\]
When we put the values, we get:
 \[ \Rightarrow 512c{m^3} = {(edge)^3}\]
We can rewrite this equation as:
 \[ \Rightarrow {(edge)^3} = 512c{m^3}\]
According to the question, we have to find each edge in cm. So, we have to take out the cube root from the edge, and shift it to the other side of the equation, and we get:
 \[ \Rightarrow edge = \sqrt[3] {{512c{m^3}}}\]
Now, we need to solve it. We know that 512 is the cube of the number 8. So, cube root of 512 is 8, so we get:
 \[ \Rightarrow edge = \sqrt[3] {{8cm \times 8cm \times 8cm}}\]
Now, we will take out the cube root, and we get:
 \[ \Rightarrow edge = 8cm\]
We got the edge as \[8cm\] .
Therefore, when the volume of the cube is \[512\;c{m^3}\] , then the length of each edge in cm is \[8cm\] .
So, the correct answer is “ \[8\;cm\] ”.

Note: In Mathematics, the volume of a cube is a number that consists of cubic units, which is completely occupied by the cube. A cube is a solid 3-dimensional figure having 6 sides or 6 square faces. If we want to calculate the volume of a cube, then we have to know the dimensions. In a cube, all the sides are equal, so if we know the length of any of its sides, then we can calculate its volume.