Answer:
10,583 flexible cubes
9915 rigid cubes
Step-by-step explanation:
The equation for the surface area of a square pyramid is area of base plus perimeter of base multiplied by the slant height
Surface area = A + 1/2·p·s
The volume of the pyramid = 1/3×A×h
Where:
A = Area of the base = 20 × 20 = 400 ft²
h = The height of the pyramid = √((slant height)² - ((base side length)/2)²)
h = √(80² - (20/2)²) = 30·√7
The volume of the pyramid = 1/3*400*30·√7 = 4000·√7 ft³ = 10,583.005 ft³
If the cubes are flexible, approximately 10,583 cubes
For rigid cubes we have
Given that the height of the pyramid = 30·√7
The slope of the pyramid = 30·√7/10 = 3·√7
So an increase in height of 1 foot gives a reduction in width of 2/(3·√7)
The bottom can hold 400 cubes
The next layer can hold 19×19 = 361
3rd 361
4th 361
5th 324
6th 324
7th 324
8th 324
9th
Continuing, we get a total of about 9915 rigid cubes in the pyramid.
