Chapter 9, Problem 57EAP

(a)

To determine

Surface to volume ratios of the moon and mars and the heat difference between the two

 Solution:

The surface area volume (SAV) for the Moon and Mars = 1.954, a larger planet cools down faster than a smaller planet

 Formula used: The surface area volume ratio $=Area/volume$

Area of a spherical body = $=4\pi r^2$

Volume of the spherical body = $=(4/3)\pi r^3$

$\begin{array}{l}SAV=4\pi r^2/(4/3)\pi r^3\\ SAV=3/r\end{array}$

 Explanation:

The radius for moon and the mars are 1738 km and 3397 km

$\begin{array}{l}SA{V}_{moon}/SA{V}_{mars}=r_{mars}/r_{moon}\\ =3397/1738\\ =1.954\end{array}$

The rate at which a planet cools will be determined by its surface area to volume ratio, the larger the planet, more slowly it cools down.

(b)

To determine

Surface to volume ratios of the Earth and Venus and the heat difference between the two

 Solution:

The surface area volume (SAV) for the Venus and earth = 1.05, a larger planet cools down faster than a smaller planet