Let the side length of the first cube be x and the side length of the second cube be y.
The volume of the first cube is x^3 and the volume of the second cube is y^3.
Given that the ratio of their volumes is 64:343, we have:
x^3/y^3 = 64/343
Taking the cube root of both sides, we get:
x/y = 4/7
Now, we know that the volume of a cube is directly proportional to the cube of its side length and the length of the diagonal of a cube is √3 times the length of its side.
Therefore, the ratio of their corresponding diagonals will be:
x√3/y√3 = 4√3/7√3 = 4/7
So, the ratio of their corresponding diagonals is 4:7.
The ratio of the volumes of two cubes is 64:343. Find the ratio of their corresponding diagonals.
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