Question 18.81

51. The cult movie Them (1954) features enormous ants (8 m long by 3 m wide). We can investigate the feasibility of such a scaled-up insect by considering its oxygen consumption. A common ant, 1 cm long, needs 24 milliliters (mL) of oxygen per second for each cubic centimeter of its volume. Because an ant has no lungs, it absorbs oxygen through its “skin” at a rate of 6.2 mL per second per square centimeter. Suppose that the tissues of a scaled-up ant would have the same need for oxygen for each cubic centimeter, and that the ant’s skin could absorb oxygen at the same rate as a common ant.

  1. Compared with a common ant, how many times as large is an enormous ant’s length, surface area, and volume?
  2. What proportion of such an ant’s oxygen need could its skin supply?
  3. What can you conclude about the existence of such insects? (Adapted from George Knill and George Fawcett, Animal form or keeping your cool, Mathematics Teacher, May 1982, 395–397.)

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51.

(a) Length = 800; surface area = 640,000; volume = 512,000,000

(b) One eight-hundredth

(c) There couldn’t be any such giant ants.