simple science question? 10 points?

Question

what has larger surface area, a large rock or many small rocks added up to equal volume as the large rock, WHY?
all i need to know is why, i know anser is small rocks...10 points

Answer 1

Make reference of a large rock to a large cube and small rocks to smaller cubes.

If you put all small cubes together you get the large cubes. You realize that several surfaces of the small cubes are not exposed when you put it to form a large cubes. For instance, many small cubes inside covered up by surface small cubes are not exposed, thus their surface area not counted as the surface area of the large cube formed. Also, for small cubes on the surfaces, only 1 side of 6 sides of the small cubes is exposed. For cubes lining the edge, only 2 sides are exposed and for cubes at the 8 corners, only 3 out of 6 sides are exposed.

However, when u calculate the total area of the samll cubes, all their area of the 6 sides are added up...that makes the total surface area of small cubes greater than a large cube.

The same applies for big and small rocks

Answer 2

Take 8 cubes, each of them 1x1x1 meter, the total volume of each is = 1 m3, 8m3 in total. The total surface area of the each cube is 6 m2 (each side 1 m2, 6 sides per cube). So the total surface area is 48 m2

Now take 1 cube of 2x2x2 meters, the volume is 8 m3 (the same as 8 small ones), the total surface area is 4 m2 for each side, so 24m2 in total.

Q.E.D.

Answer 3

put them end to end in a row ...you'll figure it out from there? any ways its a start right?