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.
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.
1. Surface area of pedestal 1:
Front and back area = 20 inches * 15 inches * 2 = 600 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 15 inches * 20 inches * 2 + 20 inches * 20 inches = 500 square inches
Total surface area of pedestal 1 = 600 + 400 + 500 = 1500 square inches
2. Surface area of pedestal 2:
Front and back area = 20 inches * 11 inches * 2 = 440 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 11 inches * 20 inches * 2 + 20 inches * 20 inches = 620 square inches
Total surface area of pedestal 2 = 440 + 400 + 620 = 1460 square inches
3. Surface area of pedestal 3:
Front and back area = 20 inches * 7 inches * 2 = 280 square inches
Top and bottom area= 20 inches * 20 inches * 2 = 400 square inches
Side area = 7 inches * 20 inches * 2 + 20 inches * 20 inches = 540 square inches
Total surface area of pedestal 3 = 280 + 400 + 540 = 1220 square inches
Total surface area of the stand = Surface area of pedestal 1 + Surface area of pedestal 2 + Surface area of pedestal 3
= 1500 + 1460 + 1220
= 4180 square inches
Therefore, the total surface area of the stand is 4180 square inches.
That is incorrect. Listen up. Eah pedestal has the same width and depth, which his twenty. However, Pedestal one is 15, pedestal 2 is 11 and pedestal three is 7 in height. Find the surface area.
To find the total surface area of the stand with the pedestals, we need to calculate the surface area of each pedestal and then add them together.
1. Surface area of pedestal 1:
Front and back area = 20 inches * 15 inches * 2 = 600 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 15 inches * 20 inches * 2 + 20 inches * 20 inches = 700 square inches
Total surface area of pedestal 1 = 600 + 400 + 700 = 1700 square inches
2. Surface area of pedestal 2:
Front and back area = 20 inches * 11 inches * 2 = 440 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 11 inches * 20 inches * 2 + 20 inches * 20 inches = 620 square inches
Total surface area of pedestal 2 = 440 + 400 + 620 = 1460 square inches
3. Surface area of pedestal 3:
Front and back area = 20 inches * 7 inches * 2 = 280 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 7 inches * 20 inches * 2 + 20 inches * 20 inches = 540 square inches
Total surface area of pedestal 3 = 280 + 400 + 540 = 1220 square inches
Total surface area of the stand = Surface area of pedestal 1 + Surface area of pedestal 2 + Surface area of pedestal 3
= 1700 + 1460 + 1220
= 4380 square inches
Therefore, the total surface area of the stand with the pedestals is 4380 square inches.
surface area, not total area
My apologies for the oversight. Let's calculate the surface area of each pedestal individually:
1. Surface area of pedestal 1:
Front and back area = 20 inches * 15 inches * 2 = 600 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 15 inches * 20 inches * 2 = 600 square inches
Total surface area of pedestal 1 = 600 + 400 + 600 = 1600 square inches
2. Surface area of pedestal 2:
Front and back area = 20 inches * 11 inches * 2 = 440 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 11 inches * 20 inches * 2 = 440 square inches
Total surface area of pedestal 2 = 440 + 400 + 440 = 1280 square inches
3. Surface area of pedestal 3:
Front and back area = 20 inches * 7 inches * 2 = 280 square inches
Top and bottom area = 20 inches * 20 inches * 2 = 400 square inches
Side area = 7 inches * 20 inches * 2 = 280 square inches
Total surface area of pedestal 3 = 280 + 400 + 280 = 960 square inches
Therefore, the surface area of each pedestal is as follows:
Pedestal 1: 1600 square inches
Pedestal 2: 1280 square inches
Pedestal 3: 960 square inches
Total surface area of the stand with the pedestals is 1600 + 1280 + 960 = 3840 square inches.