Given that the ratio of side lengths for the two similar cubes is 25, we can say that the corresponding ratios for the perimeter of one face, total surface area, and volume are also 25.
1. Perimeter of one face:
The perimeter of one face of a cube is given by 4 times the length of one side. Since the ratio of side lengths is 25, the ratio of perimeters would be 4 * 25 = 100. Therefore, the perimeter of one face of the smaller cube compared to the larger cube is 100:1.
2. Total surface area:
The total surface area of a cube is given by 6 times the square of the length of one side. Since the ratio of side lengths is 25, the ratio of total surface areas would be 6 * 25^2 = 3750. Therefore, the total surface area of the smaller cube compared to the larger cube is 3750:1.
3. Volume:
The volume of a cube is given by the cube of the length of one side. Since the ratio of side lengths is 25, the ratio of volumes would be 25^3 = 15625. Therefore, the volume of the smaller cube compared to the larger cube is 15625:1.
The ratio of side lengths for two similar cubes is 25
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Determine the ratios for each of the following. Show your work or explain how you got your answers.
the perimeter of one face of the smaller cube compared to the perimeter of one face of the larger cube
the total surface area of the smaller cube compared to the total surface area of the larger cube
the volume of the smaller cube compared to the volume of the larger cube
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