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
To find the total surface area of the stand, we need to calculate the surface area of each rectangular prism and then add them together.
For the rectangular prism labeled 2:
Surface area = 2*(20*11) + 2*(20*20) + 2*(11*20) = 440 + 800 + 440 = 1680 in^2
For the rectangular prism labeled 1:
Surface area = 2*(20*15) + 2*(20*20) + 2*(15*20) = 600 + 800 + 600 = 2000 in^2
For the rectangular prism labeled 3:
Surface area = 2*(20*7) + 2*(20*20) + 2*(7*20) = 280 + 800 + 280 = 1360 in^2
Adding the surface areas of all three rectangular prisms:
Total surface area = 1680 + 2000 + 1360 = 5040 in^2
Therefore, the total surface area of the stand is 5040 square inches.