I'm trying to help my son with a math problem that totally has me stumped, and searching online is not helping.
Given two prisms with volume 1536 and 375, what is the ratio of their surface areas?
A. 8:5
B. 64:25
C. 16:25
D. 512:125
We can't determine the actual surface area from volume alone, and as far as I can tell the ratio of surface area to volume is not consistent across random prisms.
How do we figure out this problem?
FWIW, my son is 12, in the 7th grade. (and yes, this means I'm embarrassed).
Edit: More searching did give me a site with the exact same question and shows the answer is B. 64:25. Why? How?
https://quizizz.com/admin/quiz/5aea040045cff600193132c9/math-2-final-day-2
Best Answer
The answer is B: $64:25$
This is because, for similar shapes,
$$ (\text{surface ratio})^{1/2} =( \text{volume ratio})^{1/3}$$
i.e.
$$\left(\frac{64}{25}\right)^{1/2}=\left(\frac{1536}{375}\right)^{1/3}$$