Question 1061805: Cut 1 cube into 8 cubes of exactly the same size. What percent of the original cube's surface area is the surface area of a smaller cube?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you cut the cube into 8 cubes, whose volume is the same as the larger cube, then the length of each side of the smaller cubes will be one half the length of each side of the larger cube.
for example:
if the length of each side of the larger cube is x, then the volume is x^3, and if the length of each side of the smaller cubes is x/2, then the volume of each of the smaller cubes is x^3/8 which, if you multiply that by 8, you get a total volume of x^3.
so, assuming this is correct, then:
the length of a side of the larger cube is x.
the length of a side of the small cube is x/2.
the surface area of the large cube is 6 * x^2.
the surface area of the small cube is 6 * (x/2)^2 = 6 * x^2/4 = 6/4 * x^2.
the ratio of the surface area of the small cube to the surface area of the large cube is (6/4 * x^2) / (6 * x^2) which is equal to (6/4) / 6 which is equal to 1/4 which is equal to .25
the surface area of the small cube is therefore 25% of the surface area of the large cube.
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