Question

What is the edge length of the cube?

Answer 1

Hint: Volume of the cube is given and we have to find the length of edge of this cube. Now, the volume of the cube is given by multiplying length, breadth and height. But a cube has equal length, breadth and height. So, the formula for volume of cube can be given by
$ \Rightarrow $Volume of cube $ = s \times s \times s$
Using this formula, we can find the length of the cube.

Complete step-by-step solution:
In this question, we are given a cube and we have to find the length of the cube.
Volume of the cube $ = 125000i{n^2}$.
A cube has three edges: length, breadth and height.
Now, the length of each edge is equal to each other in a cube.
Let the edge of the cube be equal to s.
Therefore, the length, breadth and height of the cube will be equal to s.
Now, we are given the volume of this cube.
Volume of a cube is obtained by multiplying length, breadth and height.
So, therefore volume of this cube will be equal to s multiplied by s multiplied by s.
$ \Rightarrow $Volume of cube $ = s \times s \times s$
$ \Rightarrow s \times s \times s = 125000 \\
   \Rightarrow {s^3} = 125000 \\ $
Now, to find the value of s, we need to find the cube root of 125000.
$ \Rightarrow s = \sqrt[3]{{125000}}$
Now, when we multiply 50 3 times, we get 125000. Therefore,
$ \Rightarrow s = 50in$
Hence, length, breadth and height of the cube is $50in$.

Note: Do not confuse cube with cuboid. The difference between cube and cuboid is that all the sides of a cube are equal whereas, all the sides of a cuboid are different.
$ \Rightarrow $Volume of cube $ = {\left( {side} \right)^3}$
$ \Rightarrow $Volume of cuboid $ = $length$ \times $breadth$ \times $height