Question

PLEASE HELP ME :'(

The Memphis Pyramid is in Tennessee is a building that is in the shape of a square pyramid. The base area of the building is 349,281 square feet and the height of the pyramid is 321 feet. If you were to roll a marble from the very top of the building, how many feet would it travel to reach the bottom? Round your answer to the nearest tenth.

Answer 1

321.1 ft

Explanation:

Linear Distance

Let's imagine a square-based pyramid of side L and height H. Please refer to the image provided below where a simplified drawing of the pyramid shows the diagonal distance D that the marble has to travel to reach the base of the pyramid from the very top of it, assuming it rolls by the very center of one of the sides.

The distance can be calculated by

`\displaystyle D=\sqrt{\left((L)/(2) \right)^2+H^2}`

We need to find the length of the side of the square base. We know its area is
`349,281 ft^2`. The area of a square is

`A_s=L^2`

We solve for L

`L=√(A)=√(349,281 )=18.9\ ft`

Now we compute D

`\displaystyle D=\sqrt{\left((18.9)/(2) \right)^2+321^2}`

`\boxed{D=321.1\ ft}`