A right rectangular prism has a base with an area of `25\ \frac{1}{2}`square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism?

Height = 6 feet

Step-by-step explanation:

Given the following data;

Base area = 25½ ft²

Volume = 153 ft³

To find the height of the right rectangular prism;

Mathematically, the volume of a right rectangular prism is given by the formula;

Volume = base area * height

Substituting into the formula, we have;

153 = 25½ * height

153 = 51/2 * height

Cross-multiplying, we have;

306 = 51 * height

Height = 306/51

Height = 6 feet

Yes, fan will provide enough airflow in the ranger station.

Step-by-step explanation:

A ranger station consist of a rectangular pyramid and a rectangular prism.

So volume of air in ranger station = volume of prism + volume of a pyramid

Volume of a rectangular prism = Length×Width×height

= 10×8×8 = 640 ft³

Volume of the pyramid =

=

= 80 ft³

Total volume of the ranger station = 640 + 80 = 720 ft³

Since CFM has the airflow capacity of 1500 cubic feet per minute so one CFM will be sufficient for the volume of 720 ft³.