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missashleyn

  • 2 years ago

Can someone help me please? A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

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  1. Dido525
    • 2 years ago
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    Do you know what the volume of a pyramid is?

  2. missashleyn
    • 2 years ago
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    1/3 (b)(h)?

  3. Dido525
    • 2 years ago
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    Yep. So in the first case, what would the volume be? You to to find the ration you divide the new value by the old value right?

  4. Dido525
    • 2 years ago
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    To find the ratio*

  5. missashleyn
    • 2 years ago
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    Well I know the height, but what's the base?

  6. Dido525
    • 2 years ago
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    No need. You got \[v=\frac{ 1 }{ 3 }A*h\]

  7. Dido525
    • 2 years ago
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    h=12.

  8. Dido525
    • 2 years ago
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    Therefore: \[v=\frac{ 1 }{3 } * A *12\] = \[V=4A\]

  9. Dido525
    • 2 years ago
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    Now we are given the ara of the base was increased by a factor of 5. In other words, it was multiplied by 5.

  10. missashleyn
    • 2 years ago
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    So, 20?

  11. Dido525
    • 2 years ago
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    Ratios mean you divide, not multiply.

  12. missashleyn
    • 2 years ago
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    Now I'm confused :(

  13. Dido525
    • 2 years ago
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    About?

  14. missashleyn
    • 2 years ago
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    I thought you said it was multiplied by 5?

  15. Dido525
    • 2 years ago
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    Haha, yeah for the new volume. But when you find a ration you divide the new value by the old value.

  16. Dido525
    • 2 years ago
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    ratio*

  17. missashleyn
    • 2 years ago
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    So... what is the ratio of the volumes of the 2 pyramids? o.o

  18. Dido525
    • 2 years ago
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    Lol, I don't want to give you an answer :P . I would rather you understand it.

  19. Dido525
    • 2 years ago
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    Allright better explanation.

  20. Dido525
    • 2 years ago
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    It's a 1/5 ratio right?

  21. Dido525
    • 2 years ago
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    Because we scale the pyramid by a factor of 5.

  22. Dido525
    • 2 years ago
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    1:5 ratio sorry.

  23. Dido525
    • 2 years ago
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    Ignore all the other parts.

  24. missashleyn
    • 2 years ago
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    I'm seriously so confused it's not even funny! Lol okay so the dimensions are increased by a facor of 5. So you're saying the ratio of the 2 pyramids is 1:5?

  25. Dido525
    • 2 years ago
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    Ahh but remember, since this is volume, we cube that 5.

  26. Dido525
    • 2 years ago
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    1/5^3

  27. Dido525
    • 2 years ago
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    or 1:125 which can also be 1/125.

  28. missashleyn
    • 2 years ago
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    My head is starting to hurt..so I cube the ratio 1:5? WHAT? Lol you have to break it down for me all at once. I don't do step by step :b

  29. Dido525
    • 2 years ago
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    Allright.

  30. Dido525
    • 2 years ago
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    The scale factor of the Pyramid is 1:5 right? This can be re-written as 1/5 . So the ratio would be 1:5 but since we are dealing with volumes, We have to cube that ratio or in other words, 1/5^3 or 1/125. We can say the New pyramid is 125x more greater than the old pyramid.

  31. missashleyn
    • 2 years ago
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    Is that the answer or are you waiting for me to answer? Lol I don't know how to do this.

  32. Dido525
    • 2 years ago
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    What don't you understand?

  33. Dido525
    • 2 years ago
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    I want to try and help :c .

  34. missashleyn
    • 2 years ago
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    I'm confused on the entire thing lol, I mean I'd like to understand how to get the right answer so I can fully explain my answer in complete sentences but at this point my head is starting to hurt and I just want to finish it. Lol

  35. dumbcow
    • 2 years ago
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    initial dimensions; height = 12 let the square base have dimensions of 1 so initial volume = 4 new dimensions, multiply lengths by 5 height = 60 square base have sides of 5 .... so area of 25 new volume = (1/3)(25)(60) = 500 volume ratio = 500/4 = 125 does that help?

  36. dumbcow
    • 2 years ago
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    in general, the rule is that the volume ratio = (length ratio)^3 --> 5^3 = 125

  37. missashleyn
    • 2 years ago
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    Yes! Thank you both for helping me.. sorry I get confused so easily! I appreciate you both! :)

  38. dumbcow
    • 2 years ago
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    :)

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