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# Water enters a cylindrical barrel at a constant speed of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Water enters a cylindrical barrel at a constant speed of  [#permalink]

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02 Jul 2018, 00:17
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25% (medium)

Question Stats:

78% (01:43) correct 22% (01:55) wrong based on 59 sessions

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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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3327 Location: India GPA: 3.12 Re: Water enters a cylindrical barrel at a constant speed of [#permalink] ### Show Tags 02 Jul 2018, 00:55 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) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 2223 Water enters a cylindrical barrel at a constant speed of [#permalink] ### Show Tags 02 Jul 2018, 15:13 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6661 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Water enters a cylindrical barrel at a constant speed of [#permalink] ### Show Tags 04 Jul 2018, 00:53 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Water enters a cylindrical barrel at a constant speed of &nbs [#permalink] 04 Jul 2018, 00:53
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