Question

A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge.

a. Write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.

b. The packaging team decides to take one layer of blocks off the top of this package. Write an expression representing the number of blocks in the top layer of the package.

c. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an expression representing the number of blocks left behind after the top two layers are removed.

Please help!!! D:​

Answer 1

The total number of blocks in a cube is b^3. The number of blocks in the top layer is b^2. After removing two layers, the number of remaining blocks is (b-2)^3.

Step-by-step explanation:

The task involves finding the total number of blocks in a cube and then adjusting for the removal of layers from the cube.

a. Total Number of Blocks in a Cube

The total number of blocks in a cube, with b blocks along one edge, can be represented by the expression b^3. This is because a cube has three dimensions, each of which is b blocks long, so the volume, or total number of blocks, is found by multiplying these dimensions together: b*b*b.

b. Number of Blocks in the Top Layer

The number of blocks in the top layer of the package is represented by the area of one face of the cube, which is b^2. Since the top layer is one block deep, you do not multiply by b the third time.

c. Number of Blocks After Removing Two Layers

After removing two layers from the top of the cube, the remaining number of blocks is given by the volume of the smaller cube that remains, which is (b-2)^3. This accounts for the two layers removed from each dimension of the cube.