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.
Reed, could you please help me out with this?
Sorry, I never even took physics in high school; I'm not qualified in this subject.
Okay, Thanks anyway! :)
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.
2*2 = 4
2*2*2 = 8 :)
Thanks so much, Damon! :)
You are welcome.
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 !
To find the surface area of the single large cube, we need to calculate the sum of the areas of all six faces. Each face has an area equal to the square of the edge length.
The edge length of the single large cube is the same as the edge length of each sugar cube, which is 2 cm (since the sugar cubes form a 2 x 2 x 2 cube).
Therefore, the surface area of the single large cube is:
Surface Area of the large cube = 6 x (Edge Length)^2
= 6 x (2 cm)^2
= 6 x 4 cm^2
= 24 cm^2
To find the total surface area of the eight individual cubes, we need to calculate the sum of the surface areas of each cube. Each cube has six faces, so the total surface area is obtained by multiplying the surface area of a single cube by 8.
The surface area of a single cube is equal to 6 times the square of the edge length.
Surface Area of a single cube = 6 x (Edge Length)^2
= 6 x (2 cm)^2
= 6 x 4 cm^2
= 24 cm^2
Total Surface Area of the eight cubes = Surface Area of a single cube x number of cubes
= 24 cm^2 x 8
= 192 cm^2
Now, we can find the ratio of the surface area of the single large cube to the total surface area of the eight cubes:
Ratio = Surface Area of the large cube / Total Surface Area of the eight cubes
= 24 cm^2 / 192 cm^2
= 1/8
Therefore, the surface area of the single, large cube is 1/8 of the total surface area of the individual eight cubes.