Answer:
Step-by-step explanation:
Given the dimension of a square pyramid
Length of pyramid
L = 75 ft
Height of pyramid
H = 28ft
The pyramid is a square base
Then,
Volume of a pyramid is calculated using
Volume = base area × height
Since base is a square, then the area of a square is
Area = L² = 75² = 5625 ft²
Then,
Volume = base Area × height
Volume = 5625 × 28
Volume = 157,500 ft³
Then, given the rate of volume to be
dV / dt = 26,250 ft³ / hr
So, we want to find the time the system will filled the air
dV / dt = 26,250
dV = 26,250 dt
Integrate both sides
∫ dV = ∫ 26,250 dt
V = 26,250t + C
When t = 0, V = 0, initially, there is not volume of system air.
Therefore C = 0
V = 26,250t
When V = 157,500 ft³
Then,
t = V / 26,250
t = 157,500 / 26,250
t = 6 hours
So, it will take 6 hours for the system to circulate the room
