The edge of the second cube is 2 times the edge of the first cube. Find the ratio of the volume

| September 6, 2021 | education

The edge of the second cube is 2 times the edge of the first cube. Find the ratio of the volume of the first cube to the volume of the second cube.

We denote by x the length of the edge of the first cube.

According to the condition of the problem, the edge of the second cube is 2 times larger than the edge of the first cube, therefore, the length of the edge of the second cube is 2x.

Let us express the volumes of the first and second cube in terms of x.

Since the volume of any cube is equal to the edge of this cube raised to the third power, the volume of the first cube is x ^ 3, and the volume of the second cube is (2x) ^ 3 = 8 * x ^ 3.

Then the ratio of the volume of the first cube to the volume of the second cube will be:

x ^ 3 / (8 * x ^ 3) = 1/8.

Answer: the ratio of the volume of the first cube to the volume of the second cube is 1/8.



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