Question

A building in the shape of a square pyramid is being built in Las Vegas. The height of the building will be 309 feet, and a size of the base measures 250 feet. The scale model that is displayed at a convention is one fifthieth the size of the actual building. What is the volume of the scale model, rounded to the nearest tenth.
Please show work!

Answer 1

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 = $(size of the base)^2\times \frac{height}{3}$

Here, size of the base of the square pyramid = 250 feet.

And, height = 309 feet.

Therefore, the volume of the given square pyramid,

$V=(250)^2\times\frac{309}{3}$

⇒ $V=62500 \times\frac{309}{3}$

⇒ $V= \frac{19312500}{3}$ = 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.