anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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anonymous
  • anonymous
Do you know what the volume of a pyramid is?
anonymous
  • anonymous
1/3 (b)(h)?
anonymous
  • anonymous
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?

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anonymous
  • anonymous
To find the ratio*
anonymous
  • anonymous
Well I know the height, but what's the base?
anonymous
  • anonymous
No need. You got \[v=\frac{ 1 }{ 3 }A*h\]
anonymous
  • anonymous
h=12.
anonymous
  • anonymous
Therefore: \[v=\frac{ 1 }{3 } * A *12\] = \[V=4A\]
anonymous
  • anonymous
Now we are given the ara of the base was increased by a factor of 5. In other words, it was multiplied by 5.
anonymous
  • anonymous
So, 20?
anonymous
  • anonymous
Ratios mean you divide, not multiply.
anonymous
  • anonymous
Now I'm confused :(
anonymous
  • anonymous
About?
anonymous
  • anonymous
I thought you said it was multiplied by 5?
anonymous
  • anonymous
Haha, yeah for the new volume. But when you find a ration you divide the new value by the old value.
anonymous
  • anonymous
ratio*
anonymous
  • anonymous
So... what is the ratio of the volumes of the 2 pyramids? o.o
anonymous
  • anonymous
Lol, I don't want to give you an answer :P . I would rather you understand it.
anonymous
  • anonymous
Allright better explanation.
anonymous
  • anonymous
It's a 1/5 ratio right?
anonymous
  • anonymous
Because we scale the pyramid by a factor of 5.
anonymous
  • anonymous
1:5 ratio sorry.
anonymous
  • anonymous
Ignore all the other parts.
anonymous
  • anonymous
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?
anonymous
  • anonymous
Ahh but remember, since this is volume, we cube that 5.
anonymous
  • anonymous
1/5^3
anonymous
  • anonymous
or 1:125 which can also be 1/125.
anonymous
  • anonymous
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
anonymous
  • anonymous
Allright.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Is that the answer or are you waiting for me to answer? Lol I don't know how to do this.
anonymous
  • anonymous
What don't you understand?
anonymous
  • anonymous
I want to try and help :c .
anonymous
  • anonymous
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
dumbcow
  • dumbcow
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?
dumbcow
  • dumbcow
in general, the rule is that the volume ratio = (length ratio)^3 --> 5^3 = 125
anonymous
  • anonymous
Yes! Thank you both for helping me.. sorry I get confused so easily! I appreciate you both! :)
dumbcow
  • dumbcow
:)

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