How does the surface area-to-volume ratio of a 1-mm cube compare to the surface area-to-volume ratio of a 3-mm cube?

Answer 1

-2

Answer 2

The surface area-to-volume ratio of a 1-mm cube is higher than that of a 3-mm cube. As objects increase in size, their volume grows faster than their surface area, leading to a decrease in the surface area-to-volume ratio. This has implications for the exchange of nutrients and waste products with the environment.

Answer 3

Volume to surface area follows the cube-square law. For a cube with side length a, the surface area is 6*a^2 and the volume is a^3 (or a-cubed, from the name of the shape).

So a 1mm cube has a surface area of 6*1^2 = 6 sq. mm and a volume of 1^3 = 1 cu. mm.

A 3mm cube has a surface area of 6*3^2 = 6*9 = 54 sq. mm and a volume of 3^3 = 27 cu. mm.

So as you can see, when the length triples the surface area goes up by a factor of 9 (or 3 squared) while the volume goes up by a factor of 27 (or 3 cubed). Hence the cube-square law.

This law applies to any shape, spheres, cylinders, etc., not just cubes. It also applies to mass. As long as the density of an object remains the same, the surface area increases as the square of the multiplier and the mass increases as the cube of the multiplier.