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01 Nov 2019, 06:52
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C
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Difficulty:
55%
(hard)
Question Stats:
66% (02:42) correct
34%
(02:40)
wrong
based on 431
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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) \(375rπ\)
Are You Up For the Challenge: 700 Level Questions
(A) \(2.1rπ\)
(B) \(25rπ\)
(C) \(125rπ\)
(D) \(300rπ\)
(E) \(375rπ\)
Are You Up For the Challenge: 700 Level Questions
01 Nov 2019, 07:46
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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.
\(\frac{3}{4}\) 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.
General Discussion
Archit3110
Major Poster
02 Nov 2019, 04:25
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Bunuel
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
