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