SOLUTION: If the ratio of the edge of two cubes is 2:3. What is the ratio of the volumes?

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Question 227704: If the ratio of the edge of two cubes is 2:3. What is the ratio of the volumes?
Found 2 solutions by jsmallt9, drj:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
While we do not know the actual sides of the cubes, we can write variable expressions for them. And as long as the ration of our expressions is 2/3, our expressions will work.

The simplest expressions which have a ratio of 2/3 would be 2x and 3x. Now let's see how the volumes work out. V+=+s%5E3 so the volume of the cube with side 2x would be: V%5B1%5D+=+%282x%29%5E3+=+8x%5E3. And the other volume would be: V%5B2%5D+=+%283x%29%5E3+=+27x%5E3. And the ratio of these volumes would be %288x%5E3%29%2F%2827x%5E3%29+=+8%2F27

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If the ratio of the edge of two cubes is 2:3. What is the ratio of the volumes?

Step 1. Let 2x be the side or edge of cube one where x is a number.

Step 2. Let 3x be the side or edge of cube two since the ratio of the edge of two cubes is 2:3.

Step 3. Volume V1 of a cube one be given as V1=%282x%29%5E3=8x%5E3

Step 4. Volume V2 of a cube two be given as V2=%283x%29%5E3=27x%5E3

Step 5. The ratio of V1%2FV2=8x%5E3%2F27x%5E3=8%2F27

Step 6. ANSWER: The ratio of volumes for these two cubes is 8:27.

I hope the above steps were helpful.

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Respectfully,
Dr J
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