Question

The Surface Area of a square pyramid is 3600 ft2. The slant height is 80 feet and the base is 20 feet. At most how many 1 foot cubic blocks can be stuffed in the pyramid?
(*Some of the blocks might have to be cut up to fit into crevices*)

Answer 1

The number of 1 foot cubic blocks that can be stuffed in the pyramid are; 10,583 cubes

How to find the surface area of a Pyramid?

The equation for the surface area of a square pyramid is;

Surface area = A + 1/2·p·s

where;

A = area of base

p = perimeter

s = slant height

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, then there are approximately 10,583 cubes

For rigid cubes we have;

Given that the height of the pyramid = 30·√7

The slope of the pyramid = (30/10)√7 = 3·√7

A increase in height of 1 foot gives a reduction in width of 2/(3√7)

The bottom can hold 400 cubes, Then next layer can hold;

19 × 19 = 361

If we continue to iterate, we will get a total of approximately 9915 rigid cubes in the pyramid.

Read more about Pyramid Surface Area at; brainly.com/question/22744289

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