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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A cylindrical cup is used to fill a bowl tagged by: VJesus12 ##### This topic has 1 expert reply and 0 member replies ## A cylindrical cup is used to fill a bowl A cylindrical cup is used to fill a bowl, which is in the shape of a hemisphere (half of a sphere), with milk. If the radius of the cup is half the radius of the hemisphere, and the height of the cup is double its radius, what is the maximum number of cups that can fill the bowl without overflowing it? A. 2 cups B. 3 cups C. 5 cups D. 6 cups E. 9 cups The OA is A. This is a hard question to me. How can I solve it? Can any expert give a good explanation of this? Thanks in advanced. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vjesus12. Let's take a look at your question. Volume of cylindrical cup: $$V_{cy}\ =\ \pi\cdot r^2\cdot h.$$ Volume of a hemisphere (bowl): $$V_{he}=\frac{2}{3}\cdot\pi\cdot R^3.$$ We have $$r=\frac{R}{2}\ \ \ \ and\ \ \ \ h=2\cdot r\ \leftrightarrow\ \ h=R.$$ Number of cups $$\frac{V_{he}}{V_{cy}}=\frac{\frac{2}{3}\pi\cdot R^3}{\pi\cdot r^2\cdot h}=\frac{\frac{2}{3}\pi\cdot R^3}{\pi\cdot\frac{R^2}{4}\cdot R}=\frac{\frac{2}{3}R^3}{\frac{R^3}{4}}=\frac{8}{3}\approx2.66667.$$ So, the maximum number of cups that can fill the bowl without overflowing is 2. When the third cup is poured, the milk overflows. So, the correct answer is A. I hope this explanation may help you. I'm available if you'd like a follow up. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • FREE GMAT Exam Know how you'd score today for$0

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