A small shipping crate is a cube with a side length of 8 inches and a surface area of 384 square inches. A large shipping crate has a surface area of 864 square inches.

Question

What is the side length of the large crate?

Answer 1

area = 4 pi r^2
volume = 4/3 pi r^3

So, for any sphere, the area:volume ratio is 3/r

However, I suspect that you garbled the question. Since area varies as the square of the diameter, if the diameters are in the ratio 3/4,

area is in the ratio (3/4)^2
volume is in the ratio (3/4)^3

Answer 2

no that's how the question is asked

Answer 3

where did the cylinder come from?
Area grows as the square of the scale. So,

864/384 = s^2/8^2
s = 12