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cubes percentage increase

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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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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 = 6e².
Volume of a cube = e³

Big cube:
Surface area = 6(4²).

Small cubes:
Since the volume of the big cube = 4³, and the volume of each of the smaller cubes = 1³, the number of smaller cubes = 4³/1³ = 4³.
Surface area of each smaller cube = 6(1²) = 6.
Total surface area of all 64 smaller cubes = 6(4³).

Increase in surface area = 6(4³) - 6(4²) = 6(4²)(4-1) = 18(4²).
Increase/Original * 100 = 18(4²) / 6(4²) * 100 = 300.

The correct answer is D.
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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 = 6a²
Before cutting the cube, side of cube = 4 cm
So, its surface area = 6(4)² = 96 cm²
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 cm²

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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