Question

Two large 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 reasoning.

Is the volume of Cube B also twice that of Cube A? Explain or show reasoning.

Answer 1

Surface area equals six times side times side, because there are six faces in a cube and each face has an area of side times side. Using that equation, the surface area of cube a is six times side times side, which is 6×2×2, which equals 24. The surface area of Cube b is 6×4×4, which equals 24×4. Since the service area of Cuba be is four times the surface area of cube a, the answer to the first question is no.

Answer 2

The side length of Cube B is twice that of Cube A.

Surface area of Cube B is not twice that of Cube A.

Volume of Cube B is not twice that of Cube A.

Explanation:

Cube A is 2×2×2.

Cube B is 4×4×4.

Side length of Cube A is 2 and side length of Cube B is 4. So, the side length of Cube B is twice that of Cube A.

Surface area of a cube is

`Area=6(side)^2`

Using this formula we get

`\text{Area of Cube A}=6(2)^2=24`

`\text{Area of Cube B}=6(4)^2=96`

96 is 4 times of 24. So, surface area of Cube B is not twice that of Cube A.

Volume of a cube is

`Volume=(side)^3`

Using this formula we get

`\text{Volume of Cube A}=(2)^3=8`

`\text{Volume of Cube B}=(4)^3=64`

64 is 8 times of 8. So, volume of Cube B is not twice that of Cube A.