Question

aliyah is repainting a toy robot made out of two wooden cubes. she wrote the expression 6(15·15)+6(9·9)−2(9·9) for the surface area of the toy. in the expression aliyah wrote, what does the term 6(15·15) represent? the surface area of the bottom cube in the expression aliyah wrote, what does the term 6(9·9) represent? the surface area of the top cube in the expression aliyah wrote, what does the term 2(9·9) represent? the area of the overlap of the cubes the total surface area of the toy

Explanation:

First Sub - Question (What does \(6(15\cdot15)\) represent?)

A cube has 6 faces, and the area of one face of a cube with side length \(s\) is \(s\times s\). For the bottom cube with side length 15 cm, the surface area (area of 6 faces) is \(6\times(15\times15)\). So this term represents the surface area of the bottom cube.

A cube has 6 faces, and the area of one face of a cube with side length \(s\) is \(s\times s\). For the top cube with side length 9 cm, the surface area (area of 6 faces) is \(6\times(9\times9)\). So this term represents the surface area of the top cube.

When the two cubes are stacked, the overlapping region is where the bottom face of the top cube and the top face of the bottom cube meet. Each of these faces has an area of \(9\times9\), so the total area of the overlap (two faces: one from each cube) is \(2\times(9\times9)\). The total surface area of the toy would be the sum of the surface areas of the two cubes minus the overlap (since those areas are no longer on the surface). So this term represents the area of the overlap of the cubes.

Answer:

The surface area of the bottom cube

Second Sub - Question (What does \(6(9\cdot9)\) represent?)