please answer this?

Question

given 3 cubes, 3 cm., 2cm., 1 cm. on a side predict:

a. which of the cubes would have the largest surface area/volume ratio?

b. which would have the diffusing materials reach the center of the block first?

c. which would have the most effecient diffusion?

Answer 1

surface area of cube with side s: 6 * s^2
volume of cube with side s: s^3

3 cm cube:
surface area = 6 * 3^2 = 6 * 9 = 54 sq cm
volume = 3^3 = 27 cu cm
surface area to volume ratio : 54/27 or 2/1

2 cm cube:
surface area = 6 * 2^2 = 6 * 4 = 24 sq cm
volume = 2^3 = 8 cu cm
surface area to volume ratio : 24/8 or 3/1

1 cm cube:
surface area = 6 * 1^2 = 6 * 1 = 6 sq cm
volume = 1^3 = 1 cu cm
surface area to volume ratio : 6/1

a) 1 cm cube

b) 1 cm cube (the bigger the surface area to volume ratio, the more efficient the diffusion)

c) 1 cm cube (the bigger the surface area to volume ratio, the more efficient the diffusion; there's more surface, relative to volume, for the diffusion to take place)

the principle is, the smaller the side of the cube, the bigger the surface area to volume ratio.
or when you're cooking, finely chopped ingredients cook faster than huge chunks
or when ice is melting, the smaller it gets, the faster it melts

hope this helps

Answer 2

a. the largest cube would have the largest surface area to volume ratio

b. the smallest cube...it has less surface area for the material to diffuse into

c. the smallest (see above).

Answer 3

A = 3 CM

B = 2 CM

C = 1 CM

Answer 4

The Answer Is

A = 3 CM...

B = 2 CM...

C = 1 CM...