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Water enters a cylindrical barrel at a constant speed of

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New post 02 Jul 2018, 01:17
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[GMAT math practice question]

Water enters a cylindrical barrel at a constant speed of \(500 cm^3/min\), and the height of the barrel increases at a constant speed of \(10\) cm per minute. What is the approximate radius of the barrel, in centimeters?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: Water enters a cylindrical barrel at a constant speed of  [#permalink]

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New post 02 Jul 2018, 01:55
MathRevolution wrote:
[GMAT math practice question]

Water enters a cylindrical barrel at a constant speed of \(500 cm^3/min\), and the height of the barrel increases at a constant speed of \(10\) cm per minute. What is the approximate radius of the barrel, in centimeters?

A. 1
B. 2
C. 3
D. 4
E. 5


Formula used: Volume = \(\pi * r^2 * h\) where \(r\) - radius of the cylinder & \(h\) - height of the cylinder

Water in the cylindrical barrel rises 10 cm in a minute, when \(500 cm^3\) of water enters the cylinder in a minute
This also means that the height of the barrel is 10 cm when a volume of \(500 cm^3\) water enters the barrel.

Substituting values \(500 = \pi * r^2 * 10\) -> \(500 = r^2 * 31.4\) (\(\pi = 3.14\)) -> \(r^2 = \frac{500}{31.4} = 16\)(approximately)

Therefore, the approximate radius of the cylinder barrel is \(\sqrt{16} = 4\)(Option D)
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Water enters a cylindrical barrel at a constant speed of  [#permalink]

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New post 02 Jul 2018, 16:13
MathRevolution wrote:
[GMAT math practice question]

Water enters a cylindrical barrel at a constant speed of \(500 cm^3/min\), and the height of the barrel increases at a constant speed of \(10\) cm per minute. What is the approximate radius of the barrel, in centimeters?

A. 1
B. 2
C. 3
D. 4
E. 5

In one minute, the barrel gets filled with \(500 cm^3\) of water, which we use as the volume of (or in) the barrel

In that same one minute, the water level rises to \(10cm\), which we use as the barrel's height (as if barrel height= water height)

Volume of the cylindrical barrel,
\(V=πr^2h\), so
\(\frac{V}{h}=πr^2\)

\(\frac{500}{10} =πr^2\)
\(50=πr^2\)
\(\frac{50}{π}=r^2\)


Approximate: \(π\approx{3}\) and \(50\approx{48}\)
\(\frac{48}{3}=16=r^2\)
\(r\approx{\sqrt{16}}\approx{4}\)


Answer D

Ignore the units.
Volume = length * length * length, in cm\(^3\)
Divide by one length (h) in cm
Volume, \(\frac{L*L*L}{L(h)}=L*L\)= Area in cm\(^2.\) We need just the value for area. The units worked.

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Re: Water enters a cylindrical barrel at a constant speed of  [#permalink]

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New post 04 Jul 2018, 01:53
=>

Let \(r\) be the radius of the barrel.
The area of the water surface \(3.14*r^2.\)
The volume of water poured in \(1\) minute is \(10*3.14*r^2.\)
Then, \(10*3.14*r^2 = 500\) or \(31.4*r^2 = 500.\)
\(r^2 = \frac{500}{31.4} ≒ 16\).

Thus, the radius is approximately \(4\) cm.

Therefore, the answer is D.
Answer: D
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Re: Water enters a cylindrical barrel at a constant speed of &nbs [#permalink] 04 Jul 2018, 01:53
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