Q:

Compare the surface area-to-volume ratios of the moon and mars. express your answer using two significant figures.

Accepted Solution

A:
we know thatFor a spherical planet of radius r, the volume V and the surface area SA is equal to[tex] V=\frac{4}{3} *\pi *r^{3} \\ \\ SA=4*\pi *r^{2} [/tex]The
ratio of these two quantities may be written as[tex] SAV =\frac{(4*\pi*r^{2})}{(\frac{4}{3}*\pi*r^{3})} \\ \\ SAV =\frac{3}{r} [/tex]we know [tex] rMoon=1,738Km\\ rMars=3,397 Km [/tex][tex] \frac{SAV Moon}{SAV Mars} =\frac{3}{rMoon} *\frac{rMars}{3} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{rMars}{rMoon} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{3,397}{1,738} \\ \\ \frac{SAV Moon}{SAV Mars} =1.9545 [/tex]thereforethe answer is[tex] 1.9 [/tex]