Question

Suppose a wealthy entrepreneur commissions the design of a spherical spaceship to house a small group for a week in orbit around the Earth. The designer allocates 1000ft^3 for each person, plus additional 4073.5ft^3 for various necessary machines. The diameter of the ship is 26.8ft.

a. What is the volume of the spaceship?


b. For approximately how many people is the ship designed?

Answer 1

a. The volume of the spaceship is calculated through the equation,
V = 4πr³/3
Dividing the given diameter by 2 to get the radius will give us 13.4 ft. Substituting the known values to the equation,
V = 4π(13.4 ft)³/3 = 10078.64 ft³

b. If we let x be the number of people allowable in the spaceship, the equation that would best represent the scenario is,
1000x + 4073.5 = 10078.64
The value of x from the equation is 6.