Question

If each edge of a cube is doubled then how many times will its volume increase?

Answer 1

Hint: Let any variable be the side of the cube and volume of the cube is $6$ times side square and side of cube so use this concept to get the required solution.

Complete step-by-step solution:
A cube is the symmetrical $3 - $ dimensional shape; it is contained by six equal squares also, it should be either solid or hollow. It has six faces.
As we know that the cube has $6$ sides and each side representing the square.
Now, the area of the square is $ = {(side)^2}$
Also, the side which means the length of the cube be a unit.
We have given that when edge is doubled
Now we have to find: How much time will the volume of the cube change?
We can show by the figure below:

We have the first figure as a given data and what they asked to find we can find out from the second figure easily.
Already we know that the volume (V) of the cube is ${(side)^3}$
$ \Rightarrow V = {a^3}$ Unit cube.
Now it is given that the question stated as the edge of the cube is also doubled.
That is now the edge of the cube becomes $2a$.
And the volume $({V_1})$ of the cube is $ = {(2a)^3} = 8{a^3}$
$ \Rightarrow {V_1} = 8{a^3}$
So now from the equation $(1)$ we have,
$ \Rightarrow {V_1} = 8V$

Hence the new volume of the cube is $8$ times the old one.

Note: Cube has its length, breadth and height equal to each other and cube is the only convex polyhedron whose faces are all squares.
The convex hull of finitely many points, not at all on the same plane is called a convex polyhedron.
There is an example of convex polyhedra are the pyramids and cubes.