To solve the problem, we will follow the steps outlined in the questions.
Part 1: Volume of the Airplane Cabin
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Determine the radius of the airplane cabin.
The radius \( r \) is half of the diameter.
\[ r = \frac{diameter}{2} = \frac{12 \text{ feet}}{2} = 6 \text{ feet} \] -
Determine the area of the circular base of the airplane cabin.
The area \( A \) of a circle is calculated using the formula \( A = \pi r^2 \). Substituting \( r = 6 \) feet and using \( \pi \approx 3.14 \), we get:
\[ A = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ square feet} \] -
What is the length of the airplane cabin?
The length \( h \) is given as 118 feet. -
Determine the volume of the airplane cabin.
The volume \( V \) of a cylinder is calculated using the formula \( V = A \times h \). We previously found \( A = 113.04 \) square feet and \( h = 118 \) feet:
\[ V = 113.04 \times 118 = 13,357.92 \text{ cubic feet} \]
Part 2: Passenger Space
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What is the volume of the airplane cabin?
The volume from Part 1 is \( 13,357.92 \) cubic feet. -
Determine the unit rate of cubic feet per person in the airplane cabin.
The maximum number of passengers is 239. To find the unit rate, divide the volume by the number of passengers: \[ \text{Unit Rate} = \frac{13,357.92 \text{ cubic feet}}{239 \text{ passengers}} \approx 55.8 \text{ cubic feet per person} \] Rounding to the nearest whole number: \[ \text{Unit Rate} \approx 56 \text{ cubic feet per person} \]
Final Answer Summary
- Radius of the airplane cabin: 6 feet
- Area of the circular base: 113.04 square feet
- Length of the airplane cabin: 118 feet
- Volume of the airplane cabin: 13,357.92 cubic feet
- Unit rate of cubic feet per person: 56 cubic feet per person