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GEOMETRY PRISM

The VOLUME of a larger prism is 168 cubic cm. If the prisms are SIMILAR with LINEAR ratio of 3:2, what is the VOLUME of the smaller prism. Answer choices are 50, 56, 252, 126.
Since the ratio of 3/2 is a LINEAR one rather than a volume one, I took the cubed root of 168 and got 5.517. Then I solved for x in a 3/2 ratio and got 3.678. Then I set up the ratio of 5.517 : 3.678 :: 3:2. That got me 112 which I was certain was the answer. But the above choices exclude 112. What am I doing wrong? Thanks.

719 day(s) ago

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Answers (5)

168/v= (3/2)^3
v = (2/3)^3 *168
= 49.7777777= 50.............................Ans

Posted 710 dy ago

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jayteacher 		Can you explain the term of a linear ratio in terms of volume from the textbook that your are using?

Posted 717 dy ago

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V1/V2= (3/2)^3
168/V2 = 27/8
V2 =168*(8/27)
=50...............................Ans

Posted 717 dy ago

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samzappala 		Lets use a slanted cube. This cube has the same height as it does width and depth. (When figuring volume, side b is used, not side c (diagonal)). To get this volume lwh is the formula. In this case, 168^(1/3)=5.518=l,w and/or h. Since the 2nd prism-cube has lengths*2/3 or .66; 5.518*2/3=3.675. So 3.675^3=49.62 cu/cm. Stick with 50cu/cm.

Posted 718 dy ago

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matherapist 		The volume of a rectangular prism is LxWxH whether its big or small. Thus if the large prism has a volume of 168cc, = LWH, then the smaller has a volume of (2/3)Lx(2/3)Wx(2/3)H or (8/27)LWH.
The linear ratio of 3/2 means that the smaller prism has sides 2/3 that of the bigger one.

Posted 718 dy ago

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