To find the total surface area of the stand, we first need to find the surface area of each individual pedestal.
Since each pedestal is a rectangular prism, the formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the prism.
For pedestal 3:
Length = Width = x (let's call the width and length of the pedestal x)
Height = 7 inches
Surface Area of pedestal 3 = 2(x)(x) + 2(x)(7) + 2(7)(x)
Surface Area of pedestal 3 = 2x^2 + 14x + 14x
Surface Area of pedestal 3 = 2x^2 + 28x
For pedestal 2:
Length = Width = x
Height = 11 inches
Surface Area of pedestal 2 = 2(x)(x) + 2(x)(11) + 2(11)(x)
Surface Area of pedestal 2 = 2x^2 + 22x + 22x
Surface Area of pedestal 2 = 2x^2 + 44x
For pedestal 1:
Length = Width = x
Height = 15 inches
Surface Area of pedestal 1 = 2(x)(x) + 2(x)(15) + 2(15)(x)
Surface Area of pedestal 1 = 2x^2 + 30x + 30x
Surface Area of pedestal 1 = 2x^2 + 60x
Now, the total surface area of the stand is the sum of the surface areas of all three pedestals:
Total Surface Area = Surface Area of pedestal 3 + Surface Area of pedestal 2 + Surface Area of pedestal 1
Total Surface Area = (2x^2 + 28x) + (2x^2 + 44x) + (2x^2 + 60x)
Total Surface Area = 6x^2 + 132x
Therefore, the total surface area of the stand is 6x^2 + 132x square 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)
1 answer