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A sculptor is planning to make two triangular prisms out of steel. The sculptor will use △ABC   for the bases of one prism and △DEF for the bases of the other prism. The triangles are similar.

Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? Show your work.

 

Please Help Me. I feel like I understand it but then I hit a wall.

 

Thank you!

KennedyPape  Feb 9, 2018
 #1
avatar+89953 
+1

Note that the scale factor here is   36/30   = 48/40  = 6/5

 

Since the prisms are the same height....the volume of the larger one will  be  the one with the base of the  triangle on the right

 

Since the prisims are the same height...the volume of the larger prism will be :

 

(scale factor)^2  as  much as the  smaller  =

 

(6/5) *  (6/5)      =  (6/5)^2  =    36/25   as much

 

Proof

Volume of smaller prism  =  base * height  =  (1/2)(40)(30) * height  =  600 * height

Volume of the larger prism  = base * height  = (1/2) (48)(36) * height  = 864 * height

 

So

 

Ratio  of  Larger Volume to Smaller    =    864 / 600   [  the height "cancels" ] 

 

And note that    600 * (6/5)^2  = 600 *  36/25  =   864

 

Does that help  ??

 

 

 

 

cool cool cool

CPhill  Feb 9, 2018
edited by CPhill  Feb 10, 2018
 #2
avatar+211 
+1

I'm still somewhat confused. Sorry. The question askes for both triangles to have the same height so wouldn't be 40/40=36/30 or something like that and then find the volume somehow.

 

Sorry Im really bad a geometry and I really appreicate you taking the time to help me out. :) 

KennedyPape  Feb 10, 2018
 #3
avatar+89953 
0

The triangles don't have the same height.....they are bases of prisms that have the same height

 

 

cool cool cool

CPhill  Feb 10, 2018
 #4
avatar+211 
0

But the question is asking for the height to be changeded andthen find the volume of te 'new' volume.

 

-Kennedypape

 

Sorry forgot to login before posting this

KennedyPape  Feb 10, 2018
edited by Guest  Feb 10, 2018
 #5
avatar+89953 
+2

Kennedy....note that the problem says that ;

 

" Suppose the sculptor makes both prisms with the same height."

 

We are not increasing the height by the scale factor.......we are only  enlarging the base  and height of the first triangle by the scale factor of (6/5)....so the second base  is  (6/5) (6/5)  = 36/25 times as large as the first........and at each cross-section parallel to both bases, the second triangle's cross-section is always 36/25 times the first......thus....its volume will be 36/25  times the first  !!!

 

 

cool cool cool

CPhill  Feb 10, 2018

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