+327 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!
+128408 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 ??
+327 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. :)
+128408 The triangles don't have the same height.....they are bases of prisms that have the same height
+327 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
+128408 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 !!!
