Question

alyah 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 area of the overlap of the cubes the surface area of the top cube the total surface area of the toy

Explanation:

For a cube, the surface area formula is \(SA = 6s^{2}\), where \(s\) is the side - length of the cube.

• In the term \(6(15\cdot15)\), since \(15\) is the side - length of the bottom cube, \(6(15\cdot15)\) represents the surface area of the bottom cube.
• In the term \(6(9\cdot9)\), since \(9\) is the side - length of the top cube, \(6(9\cdot9)\) represents the surface area of the top cube. The term \(2(9\cdot9)\) represents the area of the two overlapping faces (one from the bottom cube and one from the top cube).

Answer:

• The term \(6(15\cdot15)\) represents the surface area of the bottom cube.
• The term \(6(9\cdot9)\) represents the surface area of the top cube.