Question

The side length of the blocks is inches, so the total surface area of the 27 blocks is 1350 in.² this is the surface area of the box.

Answer 1

The side length of the blocks is 5 inches, so the total surface area of the 27 blocks is 4050 square inches. This is 3 times the surface area of the box.

The cube box has a side length of 15 inches which contains 27 cubes inside. From this, we can say that the volume of the cube is 27 in³. Since the volume of a cube is noted as:

`V=a^3`

Where a is the length of the side, we can how many blocks are on one side of the bigger cube using this formula:

`\begin{gathered} V=a^3 \\ V=27 \\ 27=a^3 \\ 3^3=a^3 \\ a=3 \end{gathered}`

This means that there are 3 blocks on one side of the side. If we illustrate this, it would look like this:

Since the side length of the box is 15 inches and there are 3 cubes on each side, this would mean that the side length of the blocks would be:

`(15)/(3)=5`

The side length of each block is 5 inches.

Now, to solve for the total surface area of 27 blocks, we will simply use the formula for the surface area of the cube and multiply it by 27.

`\begin{gathered} SA_{\text{blocks}}=6a^2 \\ SA_{\text{blocks}}=6(5)^2 \\ SA_{\text{blocks}}=150 \\ \text{Total surface area:} \\ 150*27\text{ blocks}=4050 \end{gathered}`

The total surface of 27 blocks is 4050 in²

Solving for the surface area of the box:

`\begin{gathered} SA_{\text{box}}=6a^2 \\ SA_{\text{box}}=6(15)^2 \\ SA_{\text{box}}=1350 \end{gathered}`

The total surface area of the 27 blocks is 3 times the surface area of the box.