The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium.
Can this atrium be built in the rectangular plot of land?
The atrium with the maximum allowable radius (R), in feet, is represented in the image attached. The real atrium is possible if and only if the real radius (r) is less than the maximum allowable radius and therefore, the real volume (V), in cubic feet, must be less than than maximum possible volume (V'), in cubic feet.
First, we calculate the volume occupied by the maximum allowable radius:
V' = (8 · π / 3) · (45 ft)³
V' ≈ 763407.015 ft³
The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium. [tex]\blacksquare[/tex]
To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/13338592
