At the Olympics winners of gold, silver and bronze medals stand on a tiered pedestal as labeled in the diagram. The height of pedestal three is 7 inches the height of pedestal two is 11 inches and the height of pedestal one 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 individual pedestal and then add them together.
Let's consider the dimensions of the stand:
- Height of pedestal 1 (h1) = 15 inches
- Height of pedestal 2 (h2) = 11 inches
- Height of pedestal 3 (h3) = 7 inches
- Width of each pedestal (w) = ?
- Depth of each pedestal (d) = ?
Since the width and depth of each pedestal are equal, we can consider them to be the same value. Let's denote that value as x.
Surface area of pedestal 1:
2lw + 2lh1 + 2wh1
= 2(x^2) + 2(x)(15) + 2(x)(15)
= 2x^2 + 30x + 30x
= 2x^2 + 60x
Surface area of pedestal 2:
2(x^2) + 2(x)(11) + 2(x)(11)
= 2x^2 + 22x + 22x
= 2x^2 + 44x
Surface area of pedestal 3:
2(x^2) + 2(x)(7) + 2(x)(7)
= 2x^2 + 14x + 14x
= 2x^2 + 28x
Now, to find the total surface area of the stand, we add the surface area of all three pedestals:
Total Surface Area = 2x^2 + 60x + 2x^2 + 44x + 2x^2 + 28x
= 6x^2 + 132x
So the total surface area of the stand is 6x^2 + 132x square inches.