May you help me in Geometry question?

[KareemE937]

Copyright@ Jamboree Education Pvt.Ltd.2012:Question Number 113:
Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

[RonPurewal]

Hi there,
Please read the forum rules (top thread in every folder, including this one).

Among those rules, you'll notice the following: We need a citation of the original source for every problem. Super important, as there are many copyright-related toes to avoid stepping on.

Please provide such a citation. Thanks.

[RonPurewal]

I can tell you this much: This problem gets a lot easier if you pick specific numerical dimensions for the cans.

Can't really speak in any further detail without a source.

[KareemE937]

Hi everyone,
Sorry for that forgetfulness, the Copyright@ Jamboree Education Pvt.Ltd.2012:Question Number 113:
Thanks for your time and considerations.

I can tell you this much: This problem gets a lot easier if you pick specific numerical dimensions for the cans.

Can't really speak in any further detail without a source.

[KareemE937]

Hi There,

The original citation which I have it is: Copyright@ Jamboree Education Pvt.Ltd.2012:Question Number 113.

Thanks for your time and considerations.

Regards,

Kareem

Hi there,
Please read the forum rules (top thread in every folder, including this one).

Among those rules, you'll notice the following: We need a citation of the original source for every problem. Super important, as there are many copyright-related toes to avoid stepping on.

Please provide such a citation. Thanks.

[RonPurewal]

presumably, there are answer choices?
this is another forum rule: please reproduce the problem exactly as originally provided—including all answer choices.
i'll let it go this time, but please note for future reference. thanks.

[RonPurewal]

since i have no idea where you're actually having difficulty with this problem, here are two sketches of paths you can take through the problem.

1/
pick your own numbers:
it should be pretty clear that you can't actually find the dimensions of the oil cans. so, you can just pick them yourself.
pick a height and a radius for the small can, and then follow the directions for the large can.
then, figure out how much oil is in each one.

2/
algebra:
if the radius and height of the small can are, respectively, "r" and "h", then those of the large can are "2r" and "2h".
you can also just throw these into volume formulas and compare the results.

[RonPurewal]

if you need something more specific than the above, please post specifics of what you're having trouble with.
• what do you understand?
• what don't you understand?
• how have you tried to approach the problem?
etc.

thanks.

[KareemE937]

Hi,

first of all, thanks a lot for your reply, and kindly know that if I may have any other inquiry, I will explain in details about the difficulties which I face with the question.

I have already tried the second option to solve that problem before I send my email, but I got a different answer than the correct one.

I got the answer as $4 but it's written in the book which I mentioned earlier that it should be $8 only, so I am wondering how they got this $8?

Thanks for your time and considerations.

Regards,

Kareem

since i have no idea where you're actually having difficulty with this problem, here are two sketches of paths you can take through the problem.

if you need something more specific than the above, please post specifics of what you're having trouble with.
• what do you understand?
• what don't you understand?
• how have you tried to approach the problem?
etc.

thanks.

[RonPurewal]

if you pick random dimensions for the smaller can and then follow the directions (= double both of them), then the larger can should have 8 times the volume of the smaller can.

e.g., use the simplest numbers avaliable: r = h = 1 unit for the smaller can. then r = h = 2 units for the larger can.
the volume of the smaller can is pi•1^2•1 = pi cubic units.
the volume of the larger can is pi•2^2•2 = 8•pi cubic units.

so, the big can has 8 times the volume of the small can. (you'll get the same result with any other numbers, or indeed with variables.) since the big can is half full, that's 4 times the volume of the small can.