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.
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)
1 answer
1 answer