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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 clown blows up a spherical balloon such that its... tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## A clown blows up a spherical balloon such that its... A clown blows up a spherical balloon such that its volume increases at a constant rate. I takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches. How many seconds does it take for the radius of the balloon to increase from 3 inches to 5 inches? NOTE: The volume of a single sphere is 4/3*Ï€r^3. A. 6 B. 9 C. 24 D. 30 E. 42 The OA is E. 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. This is an interesting question. I will try to explain how to solve it. It takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches, so the volume increases from $$V_1=\frac{4\pi\left(1\right)^3}{3}=\frac{4\pi}{3}\ \ \ to\ \ V_2=\frac{4\pi\left(2\right)^3}{3}=\frac{32\pi}{3}$$ in 3 seconds. We know that the volume increases at a constant rate. So it increase at $$\frac{28\pi}{3}\ each\ 3\ \sec onds,\ or\ \frac{28\pi}{9}\ per\ \sec ond.$$ Now, $$V_3=\frac{4\pi\left(3\right)^3}{3}=36\pi\ \ and\ V_5=\frac{4\pi\left(5\right)^3}{3}=\frac{500\pi}{3}.$$ So $$V_5-V_4=\frac{500\pi}{3}-36\pi=\frac{392\pi}{3}.$$ Finally, $$\frac{\frac{392\pi}{3}}{\frac{28\pi}{9}}=\frac{3528\pi}{84\pi}=42\ .$$ It implies that it takes 42 seconds to increase the radius from 3 inches to 5 inches. The correct answer is E . I hope it can help you. Feel free to ask me again if you have a doubt. 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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