Answer: 51.5 cubic feet.
Step-by-step explanation:
Since, The height of the building will be 309 feet, and a size of the base measures 250 feet.
And, we know that the volume of the square pyramid = [tex](size of the base)^2\times \frac{height}{3}[/tex]
Here, size of the base of the square pyramid = 250 feet.
And, height = 309 feet.
Therefore, the volume of the given square pyramid,
[tex]V=(250)^2\times\frac{309}{3}[/tex]
⇒ [tex]V=62500 \times\frac{309}{3}[/tex]
⇒ [tex]V= \frac{19312500}{3}[/tex] = 6437500 cubic feet.
Again according to the question,
The scale model that is displayed at a convention is one fiftieth the size of the actual building.
Therefore, Volume of the scale model = the volume of the given square pyramid/125000
= 6437500/125000= 51.5 cubic feet.
Thus, the volume of the scale model is 51.5 cubic feet.
