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Chapter 1: 20 (page 28)

Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? (b) What would the diameter (in meters) of the space station have to be to contain all this air?

Short Answer

Expert verified

(a) The volume of air taken by the astronaut was 12614.4 cubic meter.

(b) The diameter of the sphere is 28.8 m.

Step by step solution

01

Breath taken by four astronauts in year

Part (a)

The volume of air per breath = 500 cm3

The typical rate of breathing is 12 breaths per minute.

The number of breaths in a year will be,

=12breathsminute脳5256001year=6307200breaths/year

The total breath by 4 astronauts will be,

=4脳6307200breaths/year=25228800breaths/year

The total volume breath in by the four astronauts will be,

=25228800breaths/year脳500cm3脳1m3106cm3=12614.4m3

Thus, the volume of air breathed in by the four astronauts is 12614.4 m3.

02

Calculation for diameter

The diameter of sphere can be calculated as,

V=16蟺诲312614.4m3=16蟺诲3d=28.8m

Thus, the diameter of sphere is 28.8 m.

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