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.
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