Question

I see the answer but what is the thought process? thank you!

24) You put a single cube of food that measures 10 mm X 10 mm X 10 mm in your mouth. Its surface area (SA) therefore is 600 mm . If your teeth chew this single piece into small cubes that measure 1 mm X 1 mm X 1 mm. What will be the total surface area of all the small cubes? A) 6 mm B) 600 mm C) 1000 mm D) 6000 mm E) 1,000,000 mm

Answer 1

Volume of cubic food a^3 = 10X10X10 = 1000 mm3
SA of cubic food 6a^2 = 6 X 10^2 = 600 mm2

If we decrease the volume or size of the cube it will increase the surface area of the cubes.
Consider the rubiks cube playing game. In that we have 6 sides.
Consider the overall rubik cube has 10mm in length. So the volume is 1000mm3.
It has 6 sides so SA is 6X10^2 = 600mm2.

Next in that we have 27 small piece that consider has a 1mm length. In that small piece we have lot of surface area now compare to 1 whole rubiks cube.

So if we decrease the size of cube there is increase in surface area by same factor how much we are decreasing.

Here we are decreasing 10mm to 1mm.
So the SA increase fromm 600 to 6000mm2.