Chapter 5.2, Problem 23E

Reminder Round all answers to two decimal places unless otherwise indicated.

Giants Ants and Spiders Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. (Of course, they are in the end defeated by the hero and heroine.) biologists use power function as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas the cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed “radiation” is enlarged to $500$ times its normal length. (Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction.)

a. By how much will its weight be increased?

b. By how much will the cross-sectional area of its legs be increased?

c. Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? What do you think is likely to happen to this unfortunate ant? (Note: The factor by which pressure increases is given by

. $\frac{\text{Factor of increase in weight}}{\text{Factor of increase in area}})$