The Luxor Hotel in Las Vegas is a square pyramid approximately 200 m wide at the base and 105 m high.Find the volume of the building.
Question
The Luxor Hotel in Las Vegas is a square pyramid approximately 200 m wide at the base and 105 m high. Find the volume of the building.
Solution
The volume V of a pyramid is given by the formula:
V = 1/3 * base area * height
The base of the Luxor Hotel is a square with side length 200 m, so its area A is:
A = side length^2 = 200 m * 200 m = 40000 m^2
The height h of the pyramid is 105 m. Substituting A and h into the formula for V gives:
V = 1/3 * 40000 m^2 * 105 m = 1400000 m^3
So, the volume of the Luxor Hotel is approximately 1,400,000 cubic meters.
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