Volume of sphere

Question

A sphere has the minimum surface for its volume. It has a low surface area to volume ratio.

 

A) Give an example of an object that has a low surface area to volume ratio, and explain why it has such a ratio
B) Give an example of an object that has a high surface area to volume ratio, and explain why it has such a ratio

Answer 1

Let's consider the cube:

Volume = x³

T.S.A. = 6x²

Ratio of total surface area to volume = 6/x.

 

If x, the length of each side of the square faces, is a big number, then the above ratio is small, but if x is small, then the ratio 6/x is large.

 

So this ratio is not a constant, even for a single shape (similar figures).

 

My opinion is that this is not a wonderful question.