Question

Use the image to answer the question.

An illustration shows three adjoining rectangular prisms placed together and labeled from the left as 2, 1, and 3. The length of the rectangular prisms along the front base is 20 inches for each. The depth of each adjoining prism is 20 inches. The height of the rectangular prism on the left labeled 2 is 11 inches; the height of the rectangular prism in the center labeled 1 is 15 inches; the height of the rectangular prism on the right labeled 3 is 7 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)
in.2

Answer 1

4320 in.^2

Work:
- Individual surface area of a 20×20×h prism = 2(400 + 40h) = 800 + 80h.
- Sum for h = 11,15,7: 3·800 + 80(11+15+7) = 2400 + 2640 = 5040.
- Subtract twice the areas of the two shared faces: left–center = 20·11 = 220, center–right = 20·7 = 140, total shared = 360, so subtract 2·360 = 720.
- Total exposed surface area = 5040 − 720 = 4320 in.^2.