How will the volume of a cube change if its edge: 1) increase by 3 times, 2) decrease by 2 times with an explanation

Let’s use the formula for the volume of a cube:

V = a ^ 3, where a is the length of the edge of the cube.

1) If the edge is increased by 3 times, then its length will become (3 * a), the volume of the cube will be equal to:

V1 = (3 * a) ^ 3 = 27 * a ^ 3.

V1 / V = 27 * a ^ 3 / a ^ 3.

The volume has increased 27 times.

2). If the edge is reduced by 2 times, then its length will become (a / 2), the volume of the cube will be equal to:

V2 = (a / 2) ^ 3 = a3 / 8.

V2 / V = (a ^ 3/8) / a ^ 3 = 1/8.

The volume will decrease by 8 times.

Answer: 1) will increase by 27 times. 2) will decrease by 8 times.