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.

Answer 1

To find the surface area of the stand, we need to find the surface area of each pedestal and add them all together.

Since each pedestal is a rectangular prism, the surface area of one pedestal is given by the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

For pedestal 1:
l = w
w = h
h = 15
Surface area of pedestal 1 = 2lw + 2lh + 2wh
= 2(15w) + 2(15h) + 2(wh)
= 30w + 30h + 2wh
= 30w + 30h + 2w(15)
= 30w + 30(15) + 2w(15)
= 450 + 30w + 30w
= 450 + 60w

For pedestal 2:
l = w
w = h
h = 11
Surface area of pedestal 2 = 2lw + 2lh + 2wh
= 2(11w) + 2(11h) + 2(wh)
= 22w + 22h + 2wh
= 22w + 22h + 2w(11)
= 22w + 22(11) + 2w(11)
= 242 + 22w + 22w
= 242 + 44w

For pedestal 3:
l = w
w = h
h = 7
Surface area of pedestal 3 = 2lw + 2lh + 2wh
= 2(7w) + 2(7h) + 2(wh)
= 14w + 14h + 2wh
= 14w + 14h + 2w(7)
= 14w + 14(7) + 2w(7)
= 98 + 14w + 14w
= 98 + 28w

Total surface area of the stand = Surface area of pedestal 1 + surface area of pedestal 2 + surface area of pedestal 3
= (450 + 60w) + (242 + 44w) + (98 + 28w)
= 450 + 60w + 242 + 44w + 98 + 28w
= 790 + 132w

Therefore, the total surface area of the stand is 790 + 132w square units.