Question 938257
This method works only for regular tetrahedra.  Not enough info is given to calculate for irregular tetrahedra.


The formula for surface area of a regular tetrahedron is {{{SA=sqrt(3)a^2}}}

In this case we have:

{{{24=sqrt(3)a^2}}} solving for a:

{{{a^2=24/sqrt(3)}}}
{{{a=sqrt(24/sqrt(3))}}}
a=3.72 (approx.)
and

{{{a^2=96/sqrt(3)}}}
{{{a=sqrt(96/sqrt(3))}}} 
a=7.44 (approx.)

The volume for a regular tetrahedron is {{{a^3/(6(Sqrt(2)))}}}

V(1) = {{{(3.72^3)/(6sqrt(2))}}} = 6.07 
V(2) = {{{(7.44^3)/(6sqrt(2))}}} = 48.53

The ratio of volumes =V(1)/V(2) =6.07/48.53= 0.125 = 1:8
Note the ratio of edge length=1:2 or {{{(1/2)}}}
    the ratio of surface area=1:4 or {{{(1/2)^2}}}
         the ratio of volumes=1:8 or {{{(1/2)^3}}}