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# A piece of cardboard measures 30 cm by 40 cm. We can make two differen

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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A piece of cardboard measures 30 cm by 40 cm. We can make two differen  [#permalink]

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23 Jul 2018, 01:17
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25% (medium)

Question Stats:

79% (01:24) correct 21% (02:08) wrong based on 29 sessions

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[Math Revolution GMAT math practice question]

A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes?

$$A. \frac{1000}{π}$$
$$B. \frac{2000}{π}$$
$$C. \frac{3000}{π}$$
$$D. \frac{4000}{π}$$
$$E. \frac{5000}{π}$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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"  Math Revolution Discount Codes Kaplan GMAT Prep Discount Codes EMPOWERgmat Discount Codes Math Expert Joined: 02 Aug 2009 Posts: 6521 Re: A piece of cardboard measures 30 cm by 40 cm. We can make two differen [#permalink] ### Show Tags 23 Jul 2018, 04:56 MathRevolution wrote: [Math Revolution GMAT math practice question] A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes? $$A. \frac{1000}{π}$$ $$B. \frac{2000}{π}$$ $$C. \frac{3000}{π}$$ $$D. \frac{4000}{π}$$ $$E. \frac{5000}{π}$$ If the cylinder is rolled along 30... Circumference of circle so formed = 2πr=30.....r=15/π Height =40 $$V=π*\frac{15}{π}^2*40$$ For the other volume 30 and 40 will interchange So $$V=π*\frac{20}{π}^2*30$$.... Difference = $$\frac{20^2*30-15^2*40}{π}=(12000-9000)/π=3000/π$$ C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6012 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A piece of cardboard measures 30 cm by 40 cm. We can make two differen [#permalink] ### Show Tags 25 Jul 2018, 01:10 => Attachment: 7.23.png [ 4.04 KiB | Viewed 136 times ] Case $$1: 2πr = 30$$ and $$h = 40$$ $$r = \frac{15}{π}$$ The volume is $$πr^2*h = π(\frac{15}{π})^2 * 40 = \frac{( 225 * 40 )}{π} = \frac{9000}{π}.$$ Case 2: $$2πr = 40$$ and $$h = 30$$ $$r = \frac{20}{π}$$ The volume is $$πr^2*h = π(\frac{20}{π})^2 * 30 = \frac{( 400 * 30 )}{π} = \frac{12000}{π}.$$ Thus, the difference in the two volumes is $$\frac{12000}{π} - \frac{9000}{π} = \frac{3000}{π}.$$ Therefore, C is the answer. Answer: C _________________ 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: A piece of cardboard measures 30 cm by 40 cm. We can make two differen &nbs [#permalink] 25 Jul 2018, 01:10
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