Find the surface area and volume of a cube whose edge is 6 in. How many times will the surface area decrease

Find the surface area and volume of a cube whose edge is 6 in. How many times will the surface area decrease and how many times will the volume of the cube if the edge is halved?

All the faces of the cube are squares. The surface area of a cube is found as the sum of the areas of six faces:
S = 6 * a².
We find the volume of the cube by the formula:
V = a³.
By condition, the edge of the cube is 6 dm, we find the area and volume:
S1 = 6 * 6² = 6 * 36 = 216 (dm²);
V1 = 6³ = 216 (dm³).
Reducing the edge by half, we find the area and volume:
S2 = 6 * 3² = 6 * 9 = 54 (dm²);
V2 = 3³ = 27 (dm³).
Let’s compare how many times the results have decreased:
S1 / S2 = 216/54 = 4 (times);
V1 / V2 = 216/27 = 8 (times).
Answer: When the rib is reduced by half, the area of the cube has decreased by 4 times, the volume has decreased by 8 times.