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.

- anonymous

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- anonymous

Do you know what the volume of a pyramid is?

- anonymous

1/3 (b)(h)?

- 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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## More answers

- anonymous

To find the ratio*

- anonymous

Well I know the height, but what's the base?

- anonymous

No need. You got
\[v=\frac{ 1 }{ 3 }A*h\]

- anonymous

h=12.

- anonymous

Therefore:
\[v=\frac{ 1 }{3 } * A *12\]
= \[V=4A\]

- 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

So, 20?

- anonymous

Ratios mean you divide, not multiply.

- anonymous

Now I'm confused :(

- anonymous

About?

- anonymous

I thought you said it was multiplied by 5?

- anonymous

Haha, yeah for the new volume. But when you find a ration you divide the new value by the old value.

- anonymous

ratio*

- anonymous

So... what is the ratio of the volumes of the 2 pyramids? o.o

- anonymous

Lol, I don't want to give you an answer :P . I would rather you understand it.

- anonymous

Allright better explanation.

- anonymous

It's a 1/5 ratio right?

- anonymous

Because we scale the pyramid by a factor of 5.

- anonymous

1:5 ratio sorry.

- anonymous

Ignore all the other parts.

- 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

Ahh but remember, since this is volume, we cube that 5.

- anonymous

1/5^3

- anonymous

or 1:125 which can also be 1/125.

- 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

Allright.

- 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

Is that the answer or are you waiting for me to answer? Lol I don't know how to do this.

- anonymous

What don't you understand?

- anonymous

I want to try and help :c .

- 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

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

in general, the rule is that the volume ratio = (length ratio)^3
--> 5^3 = 125

- anonymous

Yes! Thank you both for helping me.. sorry I get confused so easily! I appreciate you both! :)

- dumbcow

:)

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