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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 ## If the volume of a cube with side of length 6 is equal tagged by: VJesus12 ##### This topic has 3 expert replies and 2 member replies ### Top Member ## If the volume of a cube with side of length 6 is equal If the volume of a cube with side of length 6 is equal to the volume of a rectangular solid with length 12 and width 9, then the height of the rectangular solid is (A) 2 (B) 4 (C) 6 (D) 8 (E) 9 The OA is A. What is the formula that I should use? And what are the equations needed? Legendary Member Joined 07 Sep 2017 Posted: 831 messages Followed by: 3 members Upvotes: 6 Top Reply Hello Vjesus12. We know that the side of the cube is 6, and the volume of a cube is $$V_{cube}=L^3\ \ \ \ \ \Rightarrow\ \ \ \ V_{cube}=\ 6^3=216.$$ Now, this volume is equal to the volume of a rectangular solid with length 12 and width 9. The volume of this rectangular solid is $$V_{\text{rectangular}}=L\cdot W\cdot H=12\cdot9\cdot H=108H.$$ Hence we can set the equation: $$108H\ =216\ \Rightarrow\ H=2.$$ Therefore, the correct answer is the option A. I hope it helps. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 To solve, we should know a couple volume formulas. To find volume of a cube, V = s^3, where s is the length of one side. To find volume of a rectangular solid, V = lwh, where l is length, w is width, and h is height. We know that the volume of the cube is equal to the volume of the rectangular solid, so s^3 = lwh We also know that s = 6, l = 12, and w = 9, so 6^3 = (12)(9)h We solve for h: 216 = 108h h = 2 which gives is the height of the rectangular solid, or answer choice A. _________________ 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 Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 VJesus12 wrote: If the volume of a cube with side of length 6 is equal to the volume of a rectangular solid with length 12 and width 9, then the height of the rectangular solid is (A) 2 (B) 4 (C) 6 (D) 8 (E) 9 The OA is A. What is the formula that I should use? And what are the equations needed? There's no getting around needing the equations that both Vincen and Erika used in their elegant solutions. If you were hoping to avoid doing arithmetic, once you were here: 6*6*6 = 12*9*h, you could proceed like this 6*6*6 = 2*3 * 2*3 * 2*3 = 2*2*2*3*3*3 12*9*h = 2*2*3*3*3*h Now we have 2*2*2*3*3*3 = 2*2*3*3*3*h. All we're missing on the right side of the equation is a 2. The answer is A _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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VJesus12 wrote:
If the volume of a cube with side of length 6 is equal to the volume of a rectangular solid with length 12 and width 9, then the height of the rectangular solid is

(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
The volume of the cube with a side length of 6 is 6 x 6 x 6.

If we let the height of the rectangular solid = h, then we have:

6 x 6 x 6 = 12 x 9 x h

216 = 108h

2 = h

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scott@targettestprep.com

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### Top Member

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The volume of the cube with a side length of 6 is 6 x 6 x 6.

If we let the height of the rectangular solid = h, then we have:

6 x 6 x 6 = 12 x 9 x h

216 = 108h

2 = h. Option A.

Regards!

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