Question 74239: Three adjacent faces of a box (a rectanhular parallelepiped or prism)have areas of 7, 14, and 18 square inches. Find the volume of the box.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Three adjacent faces of a box (a rectanhular parallelepiped or prism)have areas of 7, 14, and 18 square inches. Find the volume of the box.
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Let the dimensions of the box be a,b,and c.
Then:
ab=7;ac=14;bc=18
If ab=7, then a=7/b
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Substitute to get:
(7/b)c=14
Then c/b=2 or c=2b
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Substitute into bc=18 to get:
b(2b)=18
b^2=9
b=3
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If b=3 then c=2b=6
If b=3 then a=7/b=7/3
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So a=(7/3); b=3; c=6
Volume= abc = (7/3)(3)(6) = 42 cubic units
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Cheers,
Stan H.
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