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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 cylinder is placed inside a cube ##### This topic has 4 expert replies and 1 member reply ### Top Member A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described? A. 16/π B. 2π C. 8 D. 4π E. 8π Can some experts help me find the best solution in this problem? OA D ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 lheiannie07 wrote: A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described? A. 16/π B. 2π C. 8 D. 4π E. 8π The cylinder of the maximum volume that can be inscribed in a cube is one with the diameter of its base being the side length of the cube and the height also being the side length of the cube. Recall that the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. If s = side length of the cube, we have r = s/2 (since s is also the length of the diameter) and h = s. Thus, the maximum volume of the cylinder is: V = π*(s/2)^2*(s) V = π(s^3)/4 Notice that s^3 is the volume of the cube and it’s given to be 16; thus, the maximum volume of the cylinder is: V = π(16)/4 V = 4π Answer: D Master | Next Rank: 500 Posts Joined 29 Nov 2017 Posted: 100 messages Upvotes: 14 lheiannie07 wrote: A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described? A. 16/π B. 2π C. 8 D. 4π E. 8π Can some experts help me find the best solution in this problem? OA D If 2a is the side of the cube its volume would be 8a^3=16 a^3= 2 Diameter and height of the biggest cylinder that fits in cube would be 2a and its volume would be =π(a)^2X2a=2πa^3 =4 π…………( because a^3=2) hence option D is correct. . ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 If the volume of the cube is 16, each of its sides are $$\sqrt{16}$$ . The largest possible cylinder will then have a diameter AND height of $$\sqrt{16}$$. We find the area of a cylinder with $$V\ =\ \pi r^2\cdot h$$ Plugging in values (remembering that r = d/2) gives $$V\ =\ \pi\left(\frac{\sqrt{16}}{2}\right)^2\cdot\sqrt{16}$$ $$V\ =\ \pi\frac{\sqrt{16}}{2}\cdot\frac{\sqrt{16}}{2}\cdot\sqrt{16}$$ $$V\ =\ \pi\frac{16}{4}$$ $$V\ =\ 4\pi$$ _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 lheiannie07 wrote: A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described? A. 16/π B. 2π C. 8 D. 4π E. 8π The volume of the cube is 16 Volume of cube = (side length)³ So: 16 = (side length)³ So, side length = ∛16 So, the BASE of the cube is a SQUARE with dimension ∛16 by ∛16 So, the largest cylinder to fit inside the cube must have a diameter of ∛16 This means the RADIUS of the cylinder = ∛16/2 Also, since the cube has HEIGHT ∛16, the largest cylinder to fit inside the cube must have a HEIGHT of ∛16 What is the maximum possible volume of the cylinder that fits inside the cube as described? Volume = π(radius)²(height) = π(∛16/2)²(∛16) = π(16/4) = 4π = D Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described? A. 16/π B. 2π C. 8 D. 4π E. 8π Hi lheiannie07, Let's take a look at your question. Volume of the cube = 16 If x represents the side length of the cube then, $$x^3=16$$ $$x=\sqrt{16}$$ Since, the cylinder is placed inside the cube, therefore its maximum radius and height will be equal to the side length of the cube. Hence, $$Height=h=\sqrt{16}$$ $$Diameter=\sqrt{16}$$ $$Radius=r=\frac{\sqrt{16}}{2}$$ Volume of the cylinder canbe calculated using formula: $$=\pi r^2h$$ $$=\pi\left(\frac{\sqrt{16}}{2}\right)^{^{^2}}\left(\sqrt{16}\right)$$ $$=\pi\left(\frac{16^{\frac{2}{3}}}{4}\right)\left(16^{\frac{1}{3}}\right)$$ $$=\frac{\pi}{4}.\left(16^{\frac{2}{3}+\frac{1}{3}}\right)$$ $$=\frac{\pi}{4}.\left(16^{\frac{3}{3}}\right)$$ $$=\frac{\pi}{4}.\left(16\right)$$ $$=4\pi$$ Therefore, Option D is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. 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