A) The volume of a pyramid is given by the formula
V = (1/3)Bh
where B is the area of the base, and h is the height.
The Luxor pyramid has a volume of
V = (1/3)(360,000 ft²)(350 ft) = 42,000,000 ft³
= 42,000×(1000 ft³)
The hotel is designed to hold 42,000 people when filled to capacity.
B) The area of a circle is given by
A = (π/4)d²
where d is the circle's diameter.
Then the diameter can be found from the area as
d = 2√(A/π)
For the desired base area, the diameter would be
d = 2√(570,025 ft²/π
d ≈ 852 ft
The new conical hotel would have a base diameter of about 852 ft.