Question

Consider eight, eight-cubic centimeter (8 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio. Be sure to show all calculations leading to an answer.

Answer 1

Reed, could you please help me out with this?

Answer 2

Sorry, I never even took physics in high school; I'm not qualified in this subject.

Answer 3

Okay, Thanks anyway! :)

Answer 4

for similar shapes, ships and their models etc

area goes as length squared
volume goes as length cubed

twice the side length -> 4 times the area
and eight times the volume as we knew because we had to use 8 cubes :)
also note that each face shows the faces of four cubes.
They want you to see that.

Answer 5

2*2 = 4
2*2*2 = 8 :)

Answer 6

Thanks so much, Damon! :)

Answer 7

You are welcome.

Answer 8

Now think about an Oil tanker
If you increase all the dimensions by 2, twice as long, twice as wide, twice as deep,
then you can carry EIGHT times as much weight.
However you only have FOUR times the plating area rubbing aginst the bleak ocean.
So to go the same speed, you only need FOUR times the power.
Therefore, the bigger, the more cost effective.
That is why supertankers.
However think about stopping or turning one.
You have four times the power, but EIGHT times the mass.
Oh my !