Question

The roof of house is shaped like a right pyramid with a square base. The base of the pyramid measures 32ft on each side, and the roof must enclose a volume of at least 4096 ft3 of air. Calculate the minimum height for the apex of the roof

Answer 1

The answer is 11.95ft which can be rounded to 12ft.

Answer 2

To calculate the minimum height for the apex of the roof, we can use the formula for the volume of a pyramid:

Volume = (1/3) * base area * height

Given that the base of the pyramid measures 32 ft on each side, we can calculate the base area:

Base area = 32 ft * 32 ft = 1024 ft²

We know that the volume must be at least 4096 ft³. Plugging in the values, we can solve for the minimum height:

4096 ft³ = (1/3) * 1024 ft² * height

Solving for height:

height = (4096 ft³ * 3) / (1024 ft²)

height ≈ 12 ft

Therefore, the minimum height for the apex of the roof is approximately 12 ft.