It is currently 22 Jun 2017, 11:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A sculptor carved a stone into a perfect cube with faces

Author Message
VP
Joined: 25 Nov 2004
Posts: 1483
A sculptor carved a stone into a perfect cube with faces [#permalink]

### Show Tags

02 Jan 2005, 23:28
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A sculptor carved a stone into a perfect cube with faces measuring 100 square inches. He then carved this stone into a smaller cube with exactly one-third the volume of the original cube. The edge of the smaller cube measures most nearly

A. 7 inches.
B. 6 inches.
C. 5 inches.
D. 4 inches.
E. 3 inches.
Intern
Joined: 02 Jan 2005
Posts: 5
Location: Boston

### Show Tags

03 Jan 2005, 00:56
The original cube has faces with area 100 square inches, so those faces must have sides of length 10. That would give the cube a total volume of 10 ^ 3 = 1,000 cubic inches.

Since the new cube is one third the volume of the original, it has volume 1,000 / 3 = 333.33 cubic inches.

Now we have to figure out what side length would give a cube a volume of 333.33 cubic inches. Lets try some numbers from the answer choices..

7^3
= 7 * 7 * 7
= 49 * 7 =343.
Too big, but close.

6^3
= 6 * 6 * 6
= 36 * 6
= 198
Way too small.

All the other choices are even smaller, so the closest answer is 7 and the answer is A.

NOTE: The thing to understand about problems like this is that in proportional three dimensional shapes, if the volume changes by some amount, the linear measures will always change by the cubic root of that amount. In this case, the volume of the sphere changed to be 1/3 of its original, so the linear change is the cubic root of 1/3. Multiplying 10 by the cubic root of 1/3 gives 6.9 which is almost 7. Our answer checks.
_________________

Looking for a GMAT math tutor in Boston? Perhaps I can help. http://www.BostonMathTutor.com

Linear vs. Volume Change   [#permalink] 03 Jan 2005, 00:56
Display posts from previous: Sort by