Question

If each edge of a cube is doubled. How many times will volume increase?

Answer 1

Hint:
Let any variable be the side of the cube and the volume of the cube is the side cube. So, we are going to use this concept to reach the solution of the question. As we increase the side or the edge of the cube, we will find how its volume is increased.

Complete step by step solution:
As we already know that the cube has six sides and each side represents the square.
Let the length of a side of the cube be a unit.
 And we all are aware that the volume (V) of the cube is defined as $ = {\left( {{\text{Side}}} \right)^3}$
$ \Rightarrow V = {a^3}$unit cube………………………… (1)
Now, here in the question we have been given that the edge of the cube is doubled.
So, now the new edge of the new cube becomes 2a.
And the new volume (${V_1}$) of the cube with its edge being doubled is $ = {\left( {2a} \right)^3} = 8{a^3}$
$ \Rightarrow {V_1} = 8{a^3}$
Now from equation (1) we have,
$ \Rightarrow {V_1} = 8\left( V \right)$
Hence, the new volume of the cube when the edge is doubled is eight times the old volume of the cube.

So, this is the required answer.

Note:
Whenever we face such types of questions the key component is formula of volume of cube which is stated above then make the side double as given in problem statement and calculate volume of the cube as above then convert new volume in terms of old volume of the cube as above so, doing this we can easily calculate how much times the volume of the cube is increased if the edge of the cube is doubled.