SOLUTION: the areas of two similar tetrahedrons are 24 square inches and 96 square inches. find the ratio of their volumes

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: the areas of two similar tetrahedrons are 24 square inches and 96 square inches. find the ratio of their volumes       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 938257: the areas of two similar tetrahedrons are 24 square inches and 96 square inches. find the ratio of their volumes
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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%283%29a%5E2
In this case we have:
24=sqrt%283%29a%5E2 solving for a:
a%5E2=24%2Fsqrt%283%29
a=sqrt%2824%2Fsqrt%283%29%29
a=3.72 (approx.)
and
a%5E2=96%2Fsqrt%283%29
a=sqrt%2896%2Fsqrt%283%29%29
a=7.44 (approx.)
The volume for a regular tetrahedron is a%5E3%2F%286%28Sqrt%282%29%29%29
V(1) = %283.72%5E3%29%2F%286sqrt%282%29%29 = 6.07
V(2) = %287.44%5E3%29%2F%286sqrt%282%29%29 = 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 %281%2F2%29
the ratio of surface area=1:4 or %281%2F2%29%5E2
the ratio of volumes=1:8 or %281%2F2%29%5E3