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?

## If the volume of a cube with side of length 6 is equal

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### GMAT/MBA Expert

- ErikaPrepScholar
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**Posts:**503**Joined:**20 Jul 2017**Thanked**: 86 times**Followed by:**12 members**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.

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.

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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.

- DavidG@VeritasPrep
- Legendary Member
**Posts:**2666**Joined:**14 Jan 2015**Location:**Boston, MA**Thanked**: 1153 times**Followed by:**125 members**GMAT Score:**770

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 thisVJesus12 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?

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

### GMAT/MBA Expert

- Scott@TargetTestPrep
- GMAT Instructor
**Posts:**4430**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**21 members

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

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

Answer: A

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scott@targettestprep.com

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