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A cylindrical bucket, with height 10 and radius r, is 3/4 filled with

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A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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New post 01 Nov 2019, 06:52
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A cylindrical bucket, with height 10 and radius r, is 3/4 filled with water. A boy is dropping marbles with volume r/10 into the bucket at a rate of 12 per minute. How many seconds will it take before water overflows from the bucket?

(A) \(2.1rπ\)
(B) \(25rπ\)
(C) \(125rπ\)
(D) \(300rπ\)
(E) \(375rπ\)


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Re: A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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New post 01 Nov 2019, 07:46
The volume of cylinder = \(10*πr^{2}\)

\(\frac{3}{4}\) is filled with water--> \(\frac{1}{4}\) is empty= \(\frac{1}{4}*10*πr^{2}= \frac{5}{2}*πr^{2}\)

The volume of each marble = \(\frac{r}{10}\) (12 per minute = one marble per 5 seconds)


In order the cylinder to be full,
\(--> (\frac{5}{2})*πr^{2}/(\frac{r}{10})= 25πr\) marbles should be dropped.

It took 25πr*5 seconds to fill the cylinder

The answer is C.
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Re: A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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New post 02 Nov 2019, 04:25
Bunuel wrote:
A cylindrical bucket, with height 10 and radius r, is 3/4 filled with water. A boy is dropping marbles with volume r/10 into the bucket at a rate of 12 per minute. How many seconds will it take before water overflows from the bucket?

(A) \(2.1rπ\)
(B) \(25rπ\)
(C) \(125rπ\)
(D) \(300rπ\)
(E) \(375rπ\)


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total volume of the bucket = pi * r^2 * 10
which is filled 3/4 ; so 1/4th is empty
volume of bucket to be filled ; pi *r^2*10*1/4 = 5pi*r^2/4
for each rock the volume r/10
per rock 5pir^2/4 * 1/10/r = 25pir
so in 12 mins = 60/12 ; 5 seconds per rock
total time ; 25pi*r*5 = 125 pir IMO C
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Re: A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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New post 02 Nov 2019, 06:51
Bunuel wrote:
A cylindrical bucket, with height 10 and radius r, is 3/4 filled with water. A boy is dropping marbles with volume r/10 into the bucket at a rate of 12 per minute. How many seconds will it take before water overflows from the bucket?

(A) \(2.1rπ\)
(B) \(25rπ\)
(C) \(125rπ\)
(D) \(300rπ\)
(E) \(375rπ\)


Are You Up For the Challenge: 700 Level Questions


12 marbles take 1 minute = 60 seconds
--> 1 marble takes = 60/12 = 5 seconds

3/4th of cylinder is filled --> 1/4th is empty
--> Empty volume that needs to be filled = \(\frac{1}{4}*π*r^2*10 = \frac{5}{2}*π*r^2\)

Volume of 1 marble = \frac{r}{10}
Number of marbles required to fill \(\frac{5}{2}*π*r^2\) volume = \((\frac{5}{2}*π*r^2)/\frac{r}{10}\) = \(25πr\)

Time taken by 1 marble = 5 seconds
--> Time taken by \(25πr\) marbles = \(25πr*5\) = \(125rπ\)

IMO Option C
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Re: A cylindrical bucket, with height 10 and radius r, is 3/4 filled with   [#permalink] 02 Nov 2019, 06:51
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