SOLUTION: The surface areas of two similar figures are 36 in2 and 49 in2. If the volume of the smaller figure is 648 in3, what is the volume of the larger figure?

Algebra ->  Volume -> SOLUTION: The surface areas of two similar figures are 36 in2 and 49 in2. If the volume of the smaller figure is 648 in3, what is the volume of the larger figure?       Log On


   

Question 1194772: The surface areas of two similar figures are 36 in2 and 49 in2. If the volume of the smaller figure is 648 in3, what is the volume of the larger figure?

Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
s.a.
x, y, z, smaller figure dimensions
2xy%2B2yz%2B2xz=36
2%28xy%2Byz%2Bxz%29=36
xy%2Byz%2Bxz=18

s.a.
larger figure
2%28xyk%5E2%2Byzk%5E2%2Bxzk%5E2%29=49
2k%5E2%28xy%2Byz%2Bxz%29=49
substituting the expression found for smaller figure
2k%5E2%2818%29=49
k%5E2=49%2F36
highlight_green%28k=7%2F6%29

VOLUMES
smaller figure, xyz=648
larger figure, xyz%2A%287%2F6%29%5E3 or highlight%28648%287%2F6%29%5E3%29, and you can compute this if you need.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The surface areas of two similar figures are 36 in2 and 49 in2. If the volume of
the smaller figure is 648 in3, what is the volume of the larger figure?
If two 3D objects are similar, then if and only if 2 corresponding lengths on
then are in the ratio a:b, then and only then will two corresponding 2D areas
on them be in the ratio a2:b2 and then and only then will two corresponding 3D
volumes on them be in the ratio a3:b3.

Since two corresponding areas are in the ratio 36:49 then two corresponding
lengths are in the ratio of 6:7 and therefore any two corresponding volumes on
them are in the ratio 63:73 or the ratio 216:343.

216%2F648%22%22=%22%22343%2Fx

216%2Ax%22%22=%22%22343%2A648

216%2Ax%22%22=%22%22343%2A648

%28216%2Ax%29%2F216%22%22=%22%22%28343%2A648%29%2F216

%28cross%28216%29%2Ax%29%2Fcross%28216%29%5E%22%22%22%22=%22%22343%2Across%28648%29%5E3%2Fcross%28216%29%5E%22%22

x%22%22=%22%22343%2A3

x%22%22=%22%22343%2A3

x%22%22=%22%221029 in3

Edwin