Question

A gambling casino is designed in the shape of a square pyramid with a side length of 60 ft. The height of the building is 36 ft. An air filtering system can circulate air at 14,400 cu ft/hr. How long will it take the system to filter all the air in the room

Answer 1

Therefore the system will take 9 hours to filter all the air in the building.

Explanation:

Given that,

a gambling casino in the shape of squared pyramid with a side length of 60 ft.

The height of the building is 36 ft.

The volume of the building is = Area of the base ×height

= (60²×36) cubic ft

The volume of the air in the building = The volume of the building.

= (60²×36) cubic ft

An air filtering system can circulate air at 14,400 cubic ft per hour.

It means

The air filtering system can circulate 14,400 cubic ft air in 1 hour.

The air filtering system can circulate 1 cubic ft air in
`(1)/(14,400)` hour.

The air filtering system can circulate (60²×36) cubic ft air in
`(60^2* 36)/(14,440)` hours.

= 9 hours.

Therefore the system will take 9 hours to filter all the air in the building.