At the Olympics, the winners of the gold, silver, and bronze medals stand on a tiered pedestal. As labeled in the diagram, the height of pedestal 3 is 7 inches, the height of pedestal 2 is 11 inches, and the height of pedestal 1 is 15 inches. Assuming each pedestal is of equal width and depth, find the total surface area of the stand. (1 point)
First, we need to find the surface area of each pedestal, which can be calculated using the formula for the surface area of a rectangular prism:
Surface area = 2(length x width) + 2(width x height) + 2(length x height)
For Pedestal 1:
Surface area 1 = 2(x^2) + 2(x * 15) + 2(x * 15)
Surface area 1 = 4x^2 + 60x
For Pedestal 2:
Surface area 2 = 2(x^2) + 2(x * 11) + 2(x * 11)
Surface area 2 = 4x^2 + 44x
For Pedestal 3:
Surface area 3 = 2(x^2) + 2(x * 7) + 2(x * 7)
Surface area 3 = 4x^2 + 28x
The total surface area of the stand is the sum of the surface areas of the three pedestals:
Total surface area = Surface area 1 + Surface area 2 + Surface area 3
Total surface area = (4x^2 + 60x) + (4x^2 + 44x) + (4x^2 + 28x)
Total surface area = 12x^2 + 132x
Therefore, the total surface area of the stand is 12x^2 + 132x square inches.