Volume & Ratios

[roger_michael]

As simple as it is, I can't uderstand this problem. Please help.

A tin can 10 cms high contains 500 ml of water, how much would a similar can hold if it were 20 cm high?

So the ratio of the lenghts is 1 : 2...I know the volume is not the same ratio..but how i can calculate it?

Thanks,

Roger M.

[Alara533]

For CANs (assuming that it has a uniform shape...from base to top) the volume is always given as 'base area x Height'.
So if height is increased twice, volume will also increase twice!!

[gaggleofgirls]

You can prove that the ratio of the volume is the same as the ratios of the height by figuring out the area of the base...

v = pi*r^2*h
v1 (of the first can that is 10high) is pi*r^2*10 = 500
pi*r^2 = 50
so the area of the base = 50

For can 2 (20 height)
v2 = pi*r^2 *20
pi*r^2 is the same as for the first can since the base hasn't changed, so
V2 = 50(20) = 1000, which is 2:1 to 500.

-Carrie

[roger_michael]

Thank you for your posts, they are very clear and I got the same answer. However, the answer is 2 liters. This problem is from the book "How To Pass The GMAT" by Mike Byron. So I don't know i f I should trust the answers in this book. Here's a quote of the explanation:

" The ratio of corresponding lengths = 20/10, which cancels to 2/1; the ratio of the volumes will therefore equal to 2^2 / 1^2, which = 4 / 1 = 4, so the volume of the similar can will be 4 x 500 = 2,000 or 2 liters."

Is there any formula for which the volume is the square root of the lengths ?

[gaggleofgirls]

It must be an issue with the word 'similar.'

I guess the author may be using it in the sense that it is used for similar triangle, which I guess usually means that the shape is the same, but ALL the dimensions change.

Alara and I felt from the wording that only the changed (to the specific 20 from 10, therefore doubled).

If the author meant that the height doubled and the base area doubled, then yes, the volume would have quadrupled to 2 liters.

Luckily, the actual GMAT seems to be more clear in its wording. Plus, there are always 5 choices, so that can help refine the wording if the obvious choice is not present.

-Carrie