Capacity: maller jug has a capacity of 1500cm cubed and is 13cm high

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mariss

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Two jugs are similar.
The smaller jug has a capacity of 1500cm cubed and is 13cm high.
The larger jug has a capacity of 4500cm cubed.
work out the height of the larger jug.


Note: The jugs has an irregular shape, not cylindrical.


Any help please?
 
mariss said:
Two jugs are similar.
The smaller jug has a capacity of 1500cm cubed and is 13cm high.
The larger jug has a capacity of 4500cm cubed.
work out the height of the larger jug.


Note: The jugs has an irregular shape, not cylindrical.


Any help please?
Click to expand...
Similar? I'm not clear what that means in this problem.
 
Similar in the sense that jugs have the same shape but of different sizes,
 
If object A is "similar" to object B, then we can designate "corresponding parts" so that the sizes (length, area, or volume) of the corresponding parts are all in the same proportion. In particular, if A and B are similar, \(\displaystyle V_A\) and \(\displaystyle V_B\) are the volumes, \(\displaystyle h_A\) and \(\displaystyle h_B\) are the lengths of "corresponding" parts of A and B, then \(\displaystyle \frac{V_A}{h_A}= \frac{V_B}{h_B}\) so that \(\displaystyle \frac{V_A}{V_B}= \frac{h_A}{h_B}\).
 
HallsofIvy said:
If object A is "similar" to object B, then we can designate "corresponding parts" so that the sizes (length, area, or volume) of the corresponding parts are all in the same proportion. In particular, if A and B are similar, \(\displaystyle V_A\) and \(\displaystyle V_B\) are the volumes, \(\displaystyle h_A\) and \(\displaystyle h_B\) are the lengths of "corresponding" parts of A and B, then \(\displaystyle \frac{V_A}{h_A}= \frac{V_B}{h_B}\) so that \(\displaystyle \frac{V_A}{V_B}= \frac{h_A}{h_B}\).
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Prof Halls, could it also be that only the height is stretched (ie just taller) or when we say similar do all dimensions have to change from one to the other by the same percentage? Thanks for your time.
 
Jomo said:
Prof Halls, could it also be that only the height is stretched (ie just taller) or when we say similar do all dimensions have to change from one to the other by the same percentage? Thanks for your time.
Click to expand...

Well, if we follow the same logic as used for similar triangles, then I'd say, yes, all dimensions would be stretched by the same factor (perhaps it call f?). I see no reason why this wouldn't apply to a three-dimensional shape.
 
ksdhart2 said:
Well, if we follow the same logic as used for similar triangles, then I'd say, yes, all dimensions would be stretched by the same factor (perhaps it call f?). I see no reason why this wouldn't apply to a three-dimensional shape.
Click to expand...

If all the dimensions changed by a ratio Γ then the volume should change by a ratio of Γ3.

For similar triangles the ratio of the areas is Γ2.

In other words,

V1/V2 = (h1/h2)3
 
No, the relationship is between two different jugs, not between different parts of one jug.
 
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