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27 July, 19:44

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?

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  1. 27 July, 19:52
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    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.
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