# Find the surface area and volume of a cube, the edge of which is 9 dm. How many times

**Find the surface area and volume of a cube, the edge of which is 9 dm. How many times the surface area will decrease and how many times the volume of the cube, if its edge is reduced by three times.**

1) Calculate the surface area of the cube at a = 9 dm: S1 = 6 * a ^ 2 = 6 * 9 ^ 2 = 486 dm2.

2) Calculate the volume of the cube at a = 9 dm: V1 = a ^ 3 = 9 ^ 3 = 729 dm3.

3) Calculate the surface area of the cube at a = 9/3 = 3 dm: S2 = 6 * a ^ 2 = 6 * 3 ^ 2 = 54 dm2.

4) Calculate the volume of the cube at a = 9/3 = 3 dm: V ^ 2 = a ^ 3 = 3 ^ 3 = 27 dm3.

5) The ratio of the surface area of the cubes: S1 / S2 = 486/54 = 9.

6) The ratio of volumes of cubes: V1 / V2 = 729/27 = 27.

Answer: S = 486 dm2, V = 729 dm3, the area will decrease 9 times, the volume will decrease 27 times.