Chapter 7.3, Problem 47E

To determine

To Find: The surface area to the volume ratio of each penguin shown by using the cylinders to approximate their shapes. Which penguin is better occupied to live in colder environment?

Answer to Problem 47E

King penguin

Explanation of Solution

Given:

  

The ratio of the surface area to the volume of the cylinder is

  $\frac{S}{V}=\frac{2rh+2r^2}{r^{2}h}=\frac{2(h+r)}{rh}$

For Galapagos Penguin

Height = $53cm$

Radius = $6cm$

Therefore

  $\frac{S}{V}=\frac{2(53+6)}{53(6)}=0.37$

For King Penguin

Height = $94cm$

Radius = $11cm$

Therefore

  $\frac{S}{V}=\frac{2(94+11)}{94(11)}=0.2$

The king Penguin has better occupied to live in colder environment as its efficiency is low