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 the total surface area of the toy the area of the overlap of the cubes

Explanation:

Sub - question 1: What does \(6(15\cdot15)\) represent?

The surface area of a cube is given by the formula \(SA = 6s^{2}\), where \(s\) is the length of a side of the cube. For the bottom cube, the side length is \(15\) cm. The formula \(6\times(15\times15)\) is in the form of \(6s^{2}\) (since \(15\times15 = 15^{2}\)), so this term represents the surface area of the bottom cube.

The surface area of a cube is calculated as \(SA=6s^{2}\), where \(s\) is the side length. The top cube has a side length of \(9\) cm. The term \(6\times(9\times9)\) follows the formula \(6s^{2}\) (because \(9\times9 = 9^{2}\)), so this term represents the surface area of the top cube. The total surface area of the toy would be the sum of the surface areas of both cubes minus the overlapping area (which is why there is a \(- 2(9\cdot9)\) term, as the overlapping area is \(9\times9\) and it is counted twice initially, once for each cube). The area of the overlap of the cubes would be represented by \(2(9\cdot9)\) (or just \(9\times9\) for one face, but in the context of the formula, the subtraction is for the two overlapping faces), not \(6(9\cdot9)\).

Answer:

The surface area of the bottom cube

Sub - question 2: What does \(6(9\cdot9)\) represent?