which contains more potatoe skins: ten pounds of small potatoes, or ten pounds of large potatoes?

5 responses so far ↓

• 1 peri_renna // Nov 9, 2008

  Assuming all the potatoes are roughly the same shape, the weight of each potato is proportional to the cube of its length and the surface area is proportional to the square of its length. Thus, if the large potatoes are x times longer, each potato has x^3 times the mass and x^2 times the surface area.

  Since the total mass is constant, there are 1/x^3 as many large potatoes with x^2 times the surface area each, meaning x^2/x^3 = 1/x the surface area. Thus, there is more area of potato skin with the small potatoes.

• 2 sub7ime // Nov 9, 2008

  Small potatoes have more surface area given the same volume. Just imagine 10 pounds of 1-inch wide potatoes vs a single 10 pound potato.

  The point of this question is to get you to understand the relationship between volume and surface area.

• 3 John F // Nov 9, 2008

  Ten pounds of small potatoes (you have more surface area).

• 4 beartalon // Nov 9, 2008

  The surface area of a cube = 6x²

  Let’s say you had 1 large potato at 10 pounds. Surface area is 6x²

  Cut the potato into 8 pieces (2 in each dimension) to get 8 cubes of potato. Each new cube has a side of x/2.
  Surface area of all 8 = 8 * 6(x/2)² = 48x²/4 = 12x³

  If the cube was divided into 27 (3³), then the length of a side is x/3
  Surface = 27 * 6 (x/3)² = 18x²

  You can see that the numbers in relation to the original x are increasing.

  So in general, more potatoes making up the same volume will have more surface area than less potatoes making the volume.

• 5 juan dela cruz // Nov 9, 2008

  Ten pounds of small potatoes. If you cut a potato in half then cover the exposed areas with skin, then two halves would have more skin than the whole.