Geometric Representation Problem

This question is from a high school level Canadian secondary 4 text book. 

I added the question as an attachment. 

Please show and name all of the steps clearly written. 


Thank you! 

Geometry
Glegare Glegare
15
Matchmaticians Geometric Representation Problem File #1 File #1 (jpeg)
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M F H M F H
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  • M F H M F H
    0

    Thanks. Just to mention that the only assumption I made which is not 100% clear in the statement of the problem (but explicitly clarified in my answer), is that the diagonal of the top square (upper side/surface of the truncated square pyramid) must be equal to the diameter of the "cylindrical neck", given to be 6.3 cm. (I think think this is the only choice that makes sense logically.)

    • Glegare Glegare
      0

      Thanks for your work. As I am reading your answer I noticed that there was no mention of the capacity for juice in the new container when I think this was clearly stated in the problem as something that was needed to be figured out

  • M F H M F H
    0

    But capacity = amount of juice = volume ! I do use this to compute the height of the original container, and also the height of the new bottle; specifically, the volume of the lower, square prism part : V₃ = V − V₁ − V₂ , in oder to get the same capacity / total volume; which then gives the height of that part as h₃ = V₃ / (5 cm)², and the total height of the new bottle.

    • M F H M F H
      0

      I hope that's clear, else don't hesitate to ask again. (The phrase where the volume of the new container is linked to the volume of the original container is: "The volume V₃ of the square-based prism with side length L₂ = 5 cm must add up with V₁ and V₂ to the total volume V, ..." (That total volume V is the original one. I don't say more about it because the requirement "same amount of juice" meant to me obviously that the new volume must be the same as the old volume...)

  • M F H M F H
    0

    I added now "(since the new container must contain the same amount of juice as the old one)" at that point (part (3)). As I said, it seemed obvious to me, so I didn't recall it that explicitly in the first version. Sorry if that caused you trouble! (PS: the PDF isn't updated according to the latest version of the answer. Please tell me if you'd prefer an update of that file, too.)

The answer is accepted.
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