If each edge of the cube is increased by 4 times, then its volume will increase by 27 times. Find the edge of the cube?

By the condition of the problem, a cube is given.

The length of the edge of this cube will be denoted as “a” centimeters, then, with its increase by 4 centimeters, it will become equal to “4 + a” centimeters.

It is known that in this case the volume of the cube will increase 27 times.

Let’s make two equations:

1) V = a³.

2) (4 + a) ³ = 27V.

Substitute the volume of the cube into the second equation and solve it:

(4 + a) ³ = 27 * a³;

4 + a = ³√ (27 * a³);

4 + a = 3a;

4 = 3a – a;

4 = 2a;

a = 4/2 = 2 cm.

Answer: The original length of the edge of the cube is 2 centimeters.