The problem in my math book is as follows:
According to Time Magazine, men's brains on average are 10% larger than women's, even though men on average are only 8% taller. (The article mainly discusses the many differences in brain structure that likely outweigh any size differences.) If the brain scales linearly with height and men are 8% taller, what percentage larger would you expect their brains to be?
I'm really confused about this question. I've essentially figured out that the only relevant information is the last sentence, and that the scaling factor for this problem is 1.08. But I've tried plugging it in to the formulas that we have for this chapter and don't seem to get anything meaningful. The back of the book says the answer is 26% larger.
The formulas we have:
Volume of new = (scaling factor)^3 times volume of old
Area of new = (scaling factor)^2 times area of old
Any idea where I should take this from here?
Taking that at face value the brains of men would be 8% larger than women's (on average). But note the article and question does not say what they mean by size of a brain. It looks like both are confusing mass/volume with linear dimension.
If the linear dimensions scale with height then the linear dimensions would be 8% larger (or larger by a factor of 1.08), and the volume/mass would be a factor of (1.08)^3 ~= 1.26 larger, which is 26%. But the question as posted confuses the mass/volume with the linear scaling so is nonsense.