cubes percentage increase

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Tue Dec 06, 2011 5:56 am

If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

D

can you please advice

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Source: Beat The GMAT — Problem Solving | Tue Dec 06, 2011 5:56 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Dec 06, 2011 6:25 am

venmic wrote:If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

D

can you please advice

Surface area of a cube = 6eÂ².
Volume of a cube = eÂ³

Big cube:
Surface area = 6(4Â²).

Small cubes:
Since the volume of the big cube = 4Â³, and the volume of each of the smaller cubes = 1Â³, the number of smaller cubes = 4Â³/1Â³ = 4Â³.
Surface area of each smaller cube = 6(1Â²) = 6.
Total surface area of all 64 smaller cubes = 6(4Â³).

Increase in surface area = 6(4Â³) - 6(4Â²) = 6(4Â²)(4-1) = 18(4Â²).
Increase/Original * 100 = 18(4Â²) / 6(4Â²) * 100 = 300.

The correct answer is D.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Dec 06, 2011 6:46 am

venmic wrote:If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

D

can you please advice

If a is the side of a cube, then its surface area = 6aÂ²
Before cutting the cube, side of cube = 4 cm
So, its surface area = 6(4)Â² = 96 cmÂ²
Volume of the cube = a^3
Before cutting, volume of the cube = 4^3 = 64 cm^3

After cutting, side of the cube = 1 cm
After cutting, volume = 1 cm^3
Now the total volume remains same before and after cutting, so number of 1 cm cubes = 64/1 = 64
So, surface area of 64 cubes of 1 cm each = 64 * 6(1)^3 = 384 cmÂ²

Therefore, percentage increase in the surface area of the resulting cubes = [(384 - 96)/96] * 100 = [spoiler]300%[/spoiler]

The correct answer is D.

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