The Hubert H. Humphrey Metrodome in Minneapolis opened in 1982 at a cost of $55
ID: 1828836 • Letter: T
Question
The Hubert H. Humphrey Metrodome in Minneapolis opened in 1982 at a cost of $55 million. To prepare for the footings, et cetera, 3.00x105 cubic yards of dirt were removed. The Metrodome's inflatable roof covers 10.0 acres and its interior volume is 60.0x103 cubic feet. During construction, 40.0x103cubic yards of concrete, 11.9x103 tons of reinforcing steel, and 5.00x102 tons of structural steel were utilized. The roof material includes an outer layer of Teflon-coated glass and an inner layer of woven fiberglass. Given this information, answer the following:
If removed evenly over the 10.0 acres, how deep a hole would be formed as a result of the excavation?
If the two-layer fiberglass roofing material has a mass of 0.667 lbm/ft2, what is the total mass of the roof?
If 10.0 inches of wet snow collected on the roof (this happened in 1982), what is the added mass on the roof? (Assume 1 inch of water equals 10 inches of snow).
Explanation / Answer
once you have the area, you can divide it from the total volume of dirt dug to get the height dug in yards
(a) 1 acre = 4840 square yards
10 acres = 4840 square yards
300000 cubic yards/4840 square yards = 62 yards
assuming it is evenly covered first determine the total volume of snow or water on top of the roof then use the density of water (look it up on the internet) to determine the total mass of water once you have the mass, multiply it by the gravity constant in order to determine total weight of the water on the roof
(b) 10 acres = 4840 square yards = 43560 sq ft
0.667 lbm/ft^2 times 43560 ft^2 = 29055 lbm
(c) Specific weight of water is 62.4 lb/ft^3
Spread to a thickness of 1 inch, this would cover 12 ft^2
So the 10-inch snow cover has a mass of 62.4 lbm/12 ft^2
Then multiply 62.4 lbm/12 ft^2 times 43560 ft^2 = 2.265 x 10^5 lbm
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