Question

3. The company SpaceY is designing a commercial spherical spaceship and plans to start selling one-week trips

to people who want to orbit around the Earth. Spacey allocates 1,000 cubic feet per person, plus an additional
3,067.5 cubic feet for various necessary machinery. The diameter of the ship is 53.6 feet.
What is the maximum number of people who would be able to ride in the ship per trip?

Answer 1

77

Explanation:

Given the design of the spaceship is a sphere;

Volume of the spaceship = (4/3)πr^3

Volume = (4/3) × π × 26.8^3

Volume = 80639.77ft^3

1000ft^3 for each passenger

3067.5 ft^3 for machinery

Maximum number of people who can can per trip can be modeled using the relation

Volume = (space per rider × number of riders) + space for machinery

80639.77ft^3 = (1000ft^3 × number of riders) + 3067.5ft^3

(80639.77 - 3067.5)ft^3 ÷ 1000ft^3 = number of riders

77572.27ft^3 ÷ 1000 ft^3 = number of riders

77.57