Why does the surface area ratio of two spheres differ from their volume ratio?

[vikvon]

Howcome the ratio of the surface area of spheres are not equal to the ratio of volume of spheres?

For example if I had two spheres, with an aspect ratio of 1:4 when comparing surface areas, yet I have 1:8 between those same spheres when comparing volume.

This doesn't make sense to me, shouldn't the ratio be the same?

 

[gnome]

the surface area is proportional to the square of the radius

the volume is proportional to the cube of the radius

 

[damoclark]

This might help...

A line of length 2cm consists of TWO 1cm lines.

A square with side length 2cm consists of FOUR squares with side length 1cm.

A cube with side length 2cm consists of EIGHT cubes with side length 1cm.

And imagine if you took two hot coals out of a fire, one small one and a big one, which one would cool down fastest, and why?