geomerty problem : Impossible or way too easy, be the judge please.

[valenzuela]

First of all Im sorry if I dont explain the problem well enough, its kinda hard since my main language is spanish.

This problem was part of a math test I did yesterday.
So we have bucket 1 and bucket 2.


Bucket 1 has a height of 15 cm and a volume of 900 ml, Bucket 2 has the height of 20 cm. Whats the volume of bucket 2?? Both buckets are similar, and have a similar slope.
So I was like " wow wtf!!, I need to know the ratio between the radius of the big circle and the radius of the small circle. The slope the bucket has is missing [img]/images/graemlins/mad.gif[/img]"

So today my teacher gave the following answer to the problem, "all u have to do is use proportions,
15*15*15/900 = 20*20*20/X, X is 2133,333...." I was preety unconveinced by that magical propery he used. I think the property he used is good for cones and good for cylinders but not good for buckets.


So Can that problem be solved or is it impossible because the ratio of the the radius is missing?

PS: Im almost positive Im right, but I just cant prove it.

[Siegmund]

Easy, and the teacher is right.

"Similar" means that whatever the slope of the bucket is, it is the same on both buckets. Any two similar objects with one dimension in the ratio A:B must have areas A^2:B^2 volumes A^3:B^3 etc.

You say you believe this is true of cones. Are you aware that a bucket is a frustum (the base of a cone)? If it is true for cones it must also be true of buckets. The long way to solve this puzzle is to say that volume of the 15cm bucket is equal to the difference in volumes of two cones with the same slope, of heights x and x+15 cm; therefore the 20cm bucket is equal to the difference in volumes of two cones with the same slope, of heights 4/3x and 4/3x+20.

[madnak]

[ QUOTE ]
Easy, and the teacher is right.

[/ QUOTE ]

If you have two identical shapes, but one is larger than the other, this will always apply. You can take any shape you like, in any number of dimensions, and it will always hold. So long as the relative dimensions are the same, the volume relative to the dimensions will be the same.

[Silent A]

Just to really beat this into the ground ...

Your teacher is right. That is what "similar" means : all ratios of bucket 2 to bucket 1 are the same (i.e. 20/15).

This method is good for amy shape you can imagine.

[valenzuela]

My old man came up with a demostration to prove me right [img]/images/graemlins/laugh.gif[/img] , I will post if this thread receives at least two more posts.
Im way too lazy to post it but I think that if I make a post asking a question and the I disagree with every single poster then I simply have to post the demostration. But if nobody cares then its not necesarry.

[Enrique]

I am interested in seeing the proof.

[Matt R.]

Count me in for saying your teacher is right.... I'd like to hear your demonstration.

[surftheiop]

I think you got caught on the word "similar" it means something much more specific in math (as the other posters have explained) than it does in normal english usage

[madnak]

Demonstrate.

[Dale Dough]

I think valenzuela assumes that the bottom of the second bucket has the same radius as the first, just a different height, but the same slope. In that case the problem is impossible to solve.

If the bottom is 4/3 as large as well, though, the teacher is right. Does 'similar' include this definition?