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.
what is the surface area
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there are never answers for check answer quick checks
To find the total surface area of the stand, we need to calculate the surface area of each individual pedestal and then add them up.
First, let's calculate the surface area of the pedestal 3:
Surface area of one side = height * width = 7 inches * 7 inches = 49 square inches
Since there are 4 sides to the pedestal, the total surface area of pedestal 3 = 4 * 49 square inches = 196 square inches
Next, let's calculate the surface area of the pedestal 2:
Surface area of one side = height * width = 11 inches * 11 inches = 121 square inches
Since there are 4 sides to the pedestal, the total surface area of pedestal 2 = 4 * 121 square inches = 484 square inches
Finally, let's calculate the surface area of the pedestal 1:
Surface area of one side = height * width = 15 inches * 15 inches = 225 square inches
Since there are 4 sides to the pedestal, the total surface area of pedestal 1 = 4 * 225 square inches = 900 square inches
Now, add up the surface areas of all three pedestals to find the total surface area of the stand:
Total surface area = 196 + 484 + 900 = 1580 square inches
Therefore, the total surface area of the stand is 1580 square inches.
I apologize for the error. Let's try calculating the total surface area of the stand again:
Each pedestal has the same width and depth, so to calculate the total surface area, we need to account for the top surface of each pedestal, as well as the four sides of each pedestal.
The total surface area can be calculated as follows:
Surface area of pedestal 1 (top surface + 4 sides):
= (15 inches * 15 inches) + 4(15 inches * 7 inches)
= 225 square inches + 420 square inches
= 645 square inches
Surface area of pedestal 2 (top surface + 4 sides):
= (11 inches * 11 inches) + 4(11 inches * 7 inches)
= 121 square inches + 308 square inches
= 429 square inches
Surface area of pedestal 3 (top surface + 4 sides):
= (7 inches * 7 inches) + 4(7 inches * 7 inches)
= 49 square inches + 196 square inches
= 245 square inches
Total surface area of the stand:
= Surface area of pedestal 1 + Surface area of pedestal 2 + Surface area of pedestal 3
= 645 square inches + 429 square inches + 245 square inches
= 1319 square inches
Therefore, the correct total surface area of the stand is 1319 square inches. Thank you for your patience.
I apologize for the mistake. Let's calculate the total surface area of the stand correctly this time:
To find the total surface area, we need to calculate the surface area of each individual pedestal, which includes the top surface and four sides, and then add them up.
Surface area of pedestal 1:
Top surface area = 15 inches * 15 inches = 225 square inches
4 side surfaces = 2 * 15 inches * 7 inches + 2 * 15 inches * 11 inches = 330 square inches
Total surface area of pedestal 1 = 225 + 330 = 555 square inches
Surface area of pedestal 2:
Top surface area = 11 inches * 11 inches = 121 square inches
4 side surfaces = 2 * 11 inches * 7 inches + 2 * 11 inches * 15 inches = 352 square inches
Total surface area of pedestal 2 = 121 + 352 = 473 square inches
Surface area of pedestal 3:
Top surface area = 7 inches * 7 inches = 49 square inches
4 side surfaces = 2 * 7 inches * 11 inches + 2 * 7 inches * 15 inches = 244 square inches
Total surface area of pedestal 3 = 49 + 244 = 293 square inches
Total surface area of the stand = Surface area of pedestal 1 + Surface area of pedestal 2 + Surface area of pedestal 3
= 555 + 473 + 293
= 1321 square inches
Therefore, the correct total surface area of the stand is 1321 square inches. Thank you for your patience.
I apologize for the oversight. Let's calculate the total surface area of the stand again to ensure accuracy.
Let's divide the stand into three pedestals:
- Pedestal 1: Height = 15 inches
- Pedestal 2: Height = 11 inches
- Pedestal 3: Height = 7 inches
Given that each pedestal has the same width and depth, we can assume that the width and depth are equal for all pedestals.
Let's calculate the surface area of each pedestal.
1. Surface area of Pedestal 1:
Top surface area = (15 inches) * (15 inches) = 225 square inches
Side surface area = 4 * (15 inches * 7 inches) = 420 square inches
Total surface area of Pedestal 1 = 225 + 420 = 645 square inches
2. Surface area of Pedestal 2:
Top surface area = (11 inches) * (11 inches) = 121 square inches
Side surface area = 4 * (11 inches * 7 inches) = 308 square inches
Total surface area of Pedestal 2 = 121 + 308 = 429 square inches
3. Surface area of Pedestal 3:
Top surface area = (7 inches) * (7 inches) = 49 square inches
Side surface area = 4 * (7 inches * 7 inches) = 196 square inches
Total surface area of Pedestal 3 = 49 + 196 = 245 square inches
Total surface area of the stand = Surface area of Pedestal 1 + Surface area of Pedestal 2 + Surface area of Pedestal 3
= 645 + 429 + 245
= 1319 square inches
Therefore, the correct surface area of the stand is 1319 square inches. Thank you for your understanding.