SOLUTION: A theme park company is building a scale model of a killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate t

Question 1120161: A theme park company is building a scale model of a killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? What percent of change occurred from the actual tank to the mock-up of the tank?
So,I already know that the volume of the mock-up is 216 times smaller than the actual volume of the tank,since 6 cubed is 216,but I'm having trouble on the last one.I said that the mock-up is 0.00453% of the original.This is incorrect,so I changed it to 0.463% instead,since you need to multiply 100 to convert a decimal to a percent.Is this right? I'm not sure.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

In reality, the problem makes no sense at all, because of a commonly used expression which in fact has no logical meaning.

To say each dimension will be made "6 times smaller" (than the actual value x) means the dimension is going to be "x minus 6 times x", which is x-6x = -5x. Clearly a negative dimension is nonsense.

In general, the phrase "x is n times smaller than y" has no logical meaning. Unfortunately it is widely used in everyday language. It is sad that you see it in math textbooks and other resources.

What the problem really means is that each dimension is going to be 1/6 of the actual dimension. And in that case, you are right in that the volume of the model will be 1/216 of the actual volume.

So, to continue with the bad grammar that the problem uses, the answer to the first question has to be that the volume is "216 times smaller".

As for the second question, about the percent change in the volume, you tried to convert your answer 1/216 to a percent. But the 1/216 is not the fractional change; it is what is "left" after the change. The fractional change is 215/216. So presumably the answer to part b of the question is the fraction 215/216 converted to a percent.
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