If the side of the cube is increased by a factor, will its volume increase by 3 times?

Let the side of the cube be x, then the side enlarged by a times will be:

x ‘= ah.

Now let’s find the volume of the enlarged cube:

V ‘= (ax) ^ 3 = a ^ 3x ^ 3

The volume with the original side will be:

V = x ^ 3

Now we find the ratio of the increased volume to the original:

V ‘/ V = a ^ 3x ^ 3 / x ^ 3 = a ^ 3 – there will be an increase in volume.

Answer: the volume of the cube will increase a3 times.