Question

Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4. The side length of Cube B is twice that of Cube A. Is the surface area of Cube B also twice that of Cube A? Explain or show your reasoning. HELP!!

Answer 1

No, the surface area of Cube B is not twice that of Cube A.

To find the surface area of a cube, we can add up the areas of all of its faces. The surface area of a cube with side length s is given by the formula:

surface area = 6 * s^2

For Cube A, the side length is 2, so the surface area is 6 * 2^2 = 24.

For Cube B, the side length is 4, so the surface area is 6 * 4^2 = 96.

The surface area of Cube B is not twice that of Cube A, because 96 is not twice 24. Instead, the surface area of Cube B is 4 times that of Cube A. This is because the side length of Cube B is twice that of Cube A, and the surface area of a cube is directly proportional to the square of its side length. Therefore, if the side length is doubled, the surface area will be quadrupled.