Question

1. The table below shows the approximate dimensions of theLuxor Pyramid in Las Vegas and the Great Pyramid of Khufuin Egypt. Both pyramids have square bases.PyramidHeight(feet)Area of the Base(square feet)360,000Luxor350Khufu455570,025Part A: The designer of the Luxor Pyramid has allocated1000 ft of space for each person. Approximatelyhow many people is the hotel designed to hold, ifit is filled to capacity?

Answer 1

The hotel is designed to hold 42,000 people

Explanation:

The volume of a pyramid is represented by the following formula:

`\begin{gathered} V=A((h)/(3)) \\ \text{where,} \\ A=\text{Area of the base} \\ h=\text{ height} \end{gathered}`

So, find the volume of the Luxor Pyramid:

`\begin{gathered} V=360,000\cdot((350)/(3)) \\ V=42,000,000\text{ cubic feet} \end{gathered}`

Therefore, if the designer has allocated 1000 cubic feet of space for each person.

Divide the volume by the space for each person to determine how many people are the hotel designed to hold:

`\begin{gathered} \text{Capacity}=(42,000,000)/(1,000) \\ \text{Capacity}=42,000 \end{gathered}`