A cylindrical bucket, with height 10 and radius r...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

A cylindrical bucket, with height 10 and radius r...

by swerve » Thu Mar 01, 2018 5:07 am

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?

$$A.\ 2.1r\pi$$
$$B.\ 25r\pi$$
$$C.\ 125r\pi$$
$$D.\ 300r\pi$$
$$E.\ 375r\pi$$

The OA is C.

I know that the volume of cylinder=Ï€*r^2*h=Ï€r^2*10

Then?

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Mar 01, 2018 5:07 am

mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 am; Location: London, UK; Thanked: 2 times; Followed by:4 members; GMAT Score:770

by mbawisdom » Mon Mar 05, 2018 8:41 am

swerve 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?

$$A.\ 2.1r\pi$$
$$B.\ 25r\pi$$
$$C.\ 125r\pi$$
$$D.\ 300r\pi$$
$$E.\ 375r\pi$$

The OA is C.

I know that the volume of cylinder=Ï€*r^2*h=Ï€r^2*10

Then?

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Where did you get this question from? The question and answers are not correct.

This is how you want to structure your answer:

(1) What is the volume of the bucket: Vb = 10Ï€r^2 as you say above.
(2) What is the empty volume in bucket: (1/4)*Vb = 2.5Ï€r^2
(3) What is the volume of a marble: Vm = (4/3)Ï€(r/10)^3 = (4Ï€r^3)/3000
(4) How many marbles need to be dropped in the bucket such that it will push the water up to the top: Empty Volume / Volume of Marble = (2.5Ï€r^2)/((4Ï€r^3)/3000) = 7500/4r = 1875/r
(5) How often is a marble dropped into the bucket? 12 go in a minute so that is 1 every 5 seconds
(6) Time for water to be at top = # of required marbles * how often a marble is dropped in = (1875/r)*5 = 9375/r seconds
(7) Then getting technical the water won't overflow until you drop in 1 more marble so you need to add 5 seconds to the time above: 9375/r + 5 seconds

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jun 10, 2019 6:12 pm

swerve 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?

$$A.\ 2.1r\pi$$
$$B.\ 25r\pi$$
$$C.\ 125r\pi$$
$$D.\ 300r\pi$$
$$E.\ 375r\pi$$

We see that if the volume of the marbles entering the bucket exceeds the remaining 1/4 of the volume of the bucket, then the water in the bucket will overflow. Since the marbles enter the bucket at a rate of 12 per minute, the volume in the bucket is increased by 12 x r/10 = 6r/5 per minute.

Therefore, the number of minutes that needed for the water in the bucket to overflow is:

(1/4 of the volume of the bucket) / (the volume of the marbles entering the bucket per minute)

[(1/4)Ï€r^2 x 10] / (6r/5)

5Ï€r^2/2 x 5/(6r)

25Ï€r/12

Converting this to number of seconds, we have

25Ï€r/12 x 60 = 25Ï€r x 5 = 125Ï€r

Answer: C

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