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Posted by **brianna** on Sunday, December 14, 2008 at 2:15pm.

thank you.

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**Damon**, Sunday, December 14, 2008 at 2:45pmvolume proportional to scale ratio cubed

1/2*1/2*1/2 = 1/8

so

1024/8 = 128

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**brianna**, Sunday, December 14, 2008 at 2:47pmthank you Damon, but how did you get that equation?

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**Damon**, Sunday, December 14, 2008 at 2:53pmWell, you see I am a Naval Architect (ship designer)

We test ships in model basins

say the ship is k times as long as the model

then it is k times as deep

and it is k times as wide

so its volume is k * k * k = k^3 times the volume of the model :)

If you imagine the model to be made up of tiny cubes

then the ship would have to have k times as many rows along the length

and k times as many columns in width

and k times as many high

so it would need k^3 times the original number of tiny cubes to fill it .

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**brianna**, Sunday, December 14, 2008 at 3:02pmi know how to get volume,but i need to know how to find the volume of a prism. this prism is proportional to a smaller prism. but the edges of the smaller prism is half as long as the edges of the larger prism. the volume of the larger prism is 1,024 cubic feet. then the volume of the smaller prism is what? i still do not get it. by the way, thats interestinng that you design ships.

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**brianna**, Sunday, December 14, 2008 at 3:06pmare you still there?

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**Damon**, Sunday, December 14, 2008 at 3:07pmif the small prism is proportional to the large prism

Then the height of the small prism is proportional to the height of the large prism

H = k h

and the length is also proportional

L = k l

and the width is proportional

W = k w

so

L W H = k l * k w * k h = k^3 lwh

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**Damon**, Sunday, December 14, 2008 at 3:09pmThat is why I answered your cylinder problem further down the same way. You do not have to know pi.

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**brianna**, Sunday, December 14, 2008 at 3:15pmoh, but if the volume of the large prism is 1024, and the edges of the smaller prism is half the length of the larger prism, then what does k mean in your explanation?

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**Damon**, Sunday, December 14, 2008 at 3:16pmevery edge and other length measurement on the little one is 1/2 that on the big one

so k = 1/2

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**Damon**, Sunday, December 14, 2008 at 3:09pmIt does not matter the shape as long as the two objects have the same shape.

The ratio of their volumes is the scale ratio cubed.

(by the way the ratio of any equivalent areas on them is the scale ratio squared)

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**brianna**, Sunday, December 14, 2008 at 3:10pmohhh, now i get where you got that equation from, but how do i find out what thesize of the edges are, and what does k mean?

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**Damon**, Sunday, December 14, 2008 at 3:12pmThe volume of the small prism is (1/8) times the volume of the large prism.

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**Damon**, Sunday, December 14, 2008 at 3:15pmk is the scale ratio

in this case every length on the small one is 1/2 the equivalent length on the big one

so k = 1/2

and k*k*k = k^3 = 1/8

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**Damon**, Sunday, December 14, 2008 at 3:17pmNow I have to do a pretty long statistics problem for Sherri but will check back later.

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**brianna**, Sunday, December 14, 2008 at 3:19pmok

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**brianna**, Sunday, December 14, 2008 at 3:18pmoh, so the length of the small one is 1/8th? but the question says they are rectangular prisms. so they will both have 2 different measurements for the 2 different sixes of the edges

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**brianna**, Sunday, December 14, 2008 at 3:23pmDamon,im in 8th grade math, and i don't really get what you are saying. because we haven't really talked about a scale ratio is. ill wait 'till you are done with sherri.

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**Damon**, Sunday, December 14, 2008 at 3:28pmOK, I am back from the statistics

Now say we have two cubes

one is 1 cm on every edge

so its volume is 1*1*1 = 1 cm^3

Now another cube (same shape of course)

But it is 2 cm on an edge

so its volume is

2 * 2 * 2 = 8 cm^3

see what happened?

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**Damon**, Sunday, December 14, 2008 at 3:29pmThen what if the second cube were 3 cm on every edge?

volume = 3 * 3 * 3 = 3^3

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**brianna**, Sunday, December 14, 2008 at 3:32pmthey are not cubes. they are rectangular prisms. i really sorry if i confused you.

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**Damon**, Sunday, December 14, 2008 at 3:34pmNow make it harder

Let's say the first cube was 3 cm on an edge

then its volume is

3*3*3 = 27 cm^3

Now say the big one is 6 cm on an edge

its volume is

6 * 6 * 6 = 216 cm^3

BUT I would not do that

I would say

2*3 * 2*3 * 2*3 = 2^3 * 27 = 8 * 27

because my scale ratio is 2

therefore my big volume is 8 times the little one.

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**brianna**, Sunday, December 14, 2008 at 3:35pmno, they are rectangular prisms, not cubes

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**Damon**, Sunday, December 14, 2008 at 3:39pmDoes not matter shape, as long as the shape is the same. Only the size changes. The volume changes as the cube of every length measurement change ratio.

here is a sphere with 2 cm radius:

vol = (4/3) pi (2^3)

here is a sphere with 4 cm radius (k = 2)

vol = (4/3) pi (4)^3

2^3 = 8

4^3 = 64

SEE - twice the radius--> EIGHT times the volume

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**Damon**, Sunday, December 14, 2008 at 3:41pmIf every length on the big one were three times the little one, then the volume of the big one would be 3*3*3 = 27 times the volume of the little one.

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**Damon**, Sunday, December 14, 2008 at 3:44pmYes!!

You got it

1024 / 8 = 128 !!

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**brianna**, Sunday, December 14, 2008 at 3:45pmYES!! ithank you sooooo much! i would have gotten ZAP at school if i didn't finish this homework.

THANK YOU SOOOO MUCH!!!

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**Damon**, Sunday, December 14, 2008 at 3:57pmYou are welcome - now check that cylinder question down below. Same way.

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**brianna**, Sunday, December 14, 2008 at 5:32pmokay,thank you again you are pretty good at this sort of stuff

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