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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
that is inncorect
this is also incorrect
To find the total surface area of the stand, we need to calculate the surface area of each pedestal and then add them together.
Surface area of pedestal 3:
Front face = 20 inches * 7 inches = 140 square inches
Back face = 20 inches * 7 inches = 140 square inches
Left face = 11 inches * 7 inches = 77 square inches
Right face = 11 inches * 7 inches = 77 square inches
Top face = 20 inches * 20 inches = 400 square inches
Total surface area of pedestal 3 = 140 + 140 + 77 + 77 + 400 = 834 square inches
Surface area of pedestal 2:
Front face = 20 inches * 11 inches = 220 square inches
Back face = 20 inches * 11 inches = 220 square inches
Left face = 15 inches * 11 inches = 165 square inches
Right face = 15 inches * 11 inches = 165 square inches
Top face = 20 inches * 20 inches = 400 square inches
Total surface area of pedestal 2 = 220 + 220 + 165 + 165 + 400 = 1170 square inches
Surface area of pedestal 1:
Front face = 20 inches * 15 inches = 300 square inches
Back face = 20 inches * 15 inches = 300 square inches
Left face = 15 inches * 15 inches = 225 square inches
Right face = 15 inches * 15 inches = 225 square inches
Top face = 20 inches * 20 inches = 400 square inches
Total surface area of pedestal 1 = 300 + 300 + 225 + 225 + 400 = 1450 square inches
Total surface area of the stand = 834 + 1170 + 1450 = 3454 square inches
Therefore, the total surface area of the stand is 3454 square inches.
I apologize for the mistake. Let's try calculating the total surface area of the stand again:
Given:
- Height of pedestal 3 = 7 inches
- Height of pedestal 2 = 11 inches
- Height of pedestal 1 = 15 inches
- Depth of each pedestal = 20 inches (given in the illustration)
- Length of each pedestal along the front base = 20 inches (given in the illustration)
To find the total surface area of the stand, we need to calculate the surface area of each pedestal and add them together.
Surface area of each pedestal:
Front and back faces: 2 * height * depth = 2 * 20 inches * height
Side faces: 2 * height * length
Top face: length * depth
Surface area of pedestal 3:
Front and back faces: 2 * 20 * 7 = 280 square inches
Side faces: 2 * 7 * 20 = 280 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 3 = (280 + 280 + 400) = 960 square inches
Surface area of pedestal 2:
Front and back faces: 2 * 20 * 11 = 440 square inches
Side faces: 2 * 11 * 20 = 440 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 2 = (440 + 440 + 400) = 1280 square inches
Surface area of pedestal 1:
Front and back faces: 2 * 20 * 15 = 600 square inches
Side faces: 2 * 15 * 20 = 600 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 1 = (600 + 600 + 400) = 1600 square inches
Total surface area of the stand = 960 + 1280 + 1600 = 3840 square inches
Therefore, the correct total surface area of the stand is 3840 square inches. Thank you for pointing out the error.
I apologize for the mistake. Let's calculate the total surface area of the stand again using the correct dimensions and calculations:
Given:
Height of pedestal 3 = 7 inches
Height of pedestal 2 = 11 inches
Height of pedestal 1 = 15 inches
Depth of each pedestal = 20 inches
Length of each pedestal along the front base = 20 inches
To find the total surface area of the stand, we need to calculate the surface area of each pedestal and add them together.
Surface area of each pedestal:
Front and back faces: 2 * height * depth = 2 * 20 inches * height
Side faces: 2 * height * length
Top face: length * depth
Surface area of pedestal 3:
Front and back faces: 2 * 20 * 7 = 280 square inches
Side faces: 2 * 7 * 20 = 280 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 3 = 280 + 280 + 400 = 960 square inches
Surface area of pedestal 2:
Front and back faces: 2 * 20 * 11 = 440 square inches
Side faces: 2 * 11 * 20 = 440 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 2 = 440 + 440 + 400 = 1280 square inches
Surface area of pedestal 1:
Front and back faces: 2 * 20 * 15 = 600 square inches
Side faces: 2 * 15 * 20 = 600 square inches
Top face: 20 * 20 = 400 square inches
Total surface area of pedestal 1 = 600 + 600 + 400 = 1600 square inches
Total surface area of the stand = 960 + 1280 + 1600 = 3840 square inches
Therefore, the correct total surface area of the stand is 3840 square inches. Thank you for your patience.