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?

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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)   (Show Source): You can put this solution on YOUR website!
s.a.
x, y, z, smaller figure dimensions




s.a.
larger figure


substituting the expression found for smaller figure




VOLUMES
smaller figure,
larger figure, or , and you can compute this if you need.
Answer by Edwin McCravy(20056)   (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.















 in3

Edwin
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