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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 right cylinder and a cube have the same surface area... tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## A right cylinder and a cube have the same surface area... A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube? A) 6% B) 13% C) 26% D) 32% E) 35% The OA is B. Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello AAPL. Let's see. The surface area of the cylinder is: $$A_{cy}=2\pi\cdot r^2+2\pi\cdot r\cdot h$$ and the surface area of the cube is: $$A_{cu}=6L^2.$$ As the height of the cylinder is equal to its diameter, then $$h=2r,\ so\ A_{cy}=2\pi r^2+2\pi\cdot r\cdot2r=2\pi r^2+4\pi r^2=6\pi r^2.$$ Now, as the cylinder and the cube have the same surface area then $$6\pi r^2=6L^2\leftrightarrow\ \pi r^2=L^2\ \leftrightarrow\ L=r\sqrt{\pi}.$$ Now, the volumen of the cylinder and the cube are: $$V_{cy}=\pi r^2\cdot h=2\pi r^3,\ \ \ \ \ \ V_{cu}=L^3.$$ Replacing L in this last equation we get: $$V_{cu}=L^3=\left(r\sqrt{\pi}\right)^3=\pi r^3\sqrt{\pi}=\frac{2\pi r^3\sqrt{\pi}}{2}=\frac{V_{cy}\sqrt{\pi}}{2}\approx V_{cy}\cdot0.88=88\%V_{cy}.$$ That implies that the volumen of the cylinder is approximately 12% greater than the volume of the cube. Whatching the options we have that the correct answer is B. I hope this explanation may help you. Feel free to ask me again if you have any doubt. _________________ 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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