Anonymous

Consider eight two-cubic centimeter (2 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?

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Tim Cook Profile
Tim Cook answered

The easiest way to compare the two cubes in the way you describe is to perform the calculations necessary to discover their respective surface areas, and then to compare the results.

The formula to find out the surface area of a cube is:

Area = 6 x (a x a), where a is the length of one edge of the cube. Therefore, where a cube has a length of 2cm, as in your question, the calculation is as follows:

6 x (2 x 2) = 6 x 4 = 24.

The total surface area for a cube of the dimensions 2cm x 2cm  x 2cm is therefore 24cm squared.

Eight cubes of dimensions 2cm x 2cm x 2cm assembled to form one large cube would have a edge length of 4cm. The calculation is then as follows:

6 x (4 x 4) = 6 x 16 = 96cm squared

We can check this back by looking at our original single cube.

96cm squared divided by 24cm squared = 4.

By cubing the original 2cm x 2cm x 2cm, we are in effect multiplying that cube by 4, as becomes apparent visually when you assemble the larger cube. Our calculations are therefore correct.

To read other Blurtit questions about cubes, check out I Have To Find The Total Area Of A Cube With Edge 4. Can You Help? as well as What Is The Volume Of A Cube With Edge 2?

For more help on calculating the area of a cube, head over to YouTube, where there are several useful tutorials waiting to be watched, like this one:

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