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

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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01 Nov 2019, 06:52
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Difficulty:

55% (hard)

Question Stats:

60% (02:34) correct 40% (02:58) wrong based on 60 sessions

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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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Joined: 25 Jul 2018
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Re: A cylindrical bucket, with height 10 and radius r, is 3/4 filled with  [#permalink]

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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

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

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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) $$375rπ$$

Are You Up For the Challenge: 700 Level Questions

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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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
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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