Earth and moon?

Question

* Both the earth and moonaret thought to have formed with simular internal temperatures about 4.6 billion yrs ago. Both world gradually lose this internal heat to space as the heat passes out throughtheir surfaces*

Question. The diameter of the earth is about four times the diameter of the moon. How does the surface area to volume ratio of the earth compare to that of the moon?


Please explain, I don't know how to do this problem.

Answer 1

A = πR^2
De/Dm ≈ 4
Re/Rm ≈ 4
Ae/Am = π(Re)^2/π(Rm)^2 = (Re)^2/(Rm)^2
Ae/Am = (Re/Rm)^2 ≈ 4^2, or 16

Answer 2

The first part of the problem is really interesting
Anyways

Let R denote radius of Earth and r for the moon

R=4r

SA/volume ratio for radius n = 4pn^2/(4/3pn^3) = 1/(3n)

There fore ans = [1/(3R)]/[(1/3r)]=r/R = 1/4

Answer 3

Hi,

The equations for sphere surface area (SA) and volume (V) are:

SA = 4*pi*r^2
V = (4/3)*pi*r^3

Plug your numbers for earth and moon radius into these equations to get the answer.

hth.

REgards,
Chas.