SOLUTION: The side of a cube is decreased by 50%. By how much does the volume decrease? (A) 12.5% (B) 25% (C) 50% (D) 75% (E) 87.5%

Question 264867: The side of a cube is decreased by 50%. By how much does the volume decrease?
(A) 12.5% (B) 25% (C) 50% (D) 75% (E) 87.5%
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the volume of a cube is equal to s^3 = s*s*s

if you halve the volume, then the volume of the cube becomes (.5*s)^3.

(.5*s)^3 is the same as (.5)^3 * (s)^3 = .125*s^3.

.125 * 100% = 12.5%

The volume of the cube becomes 12.5% of the original volume.

The question is:

By how much does the volume decrease?

If you go from 100% of the volume to 12.5% of the volume, you have decreased by 87.5% of the original volume.

your answer would be selection E (87.5%).

As an example:

Assume the side of the cube is 4.

The volume is 4^3 = 4*4*4 = 64

Take half the side of the cube to get 2.

The volume of the cube is now 2^3 = 2*2*2 = 8.

8/64 = 1/8 = .125 * 100% = 12.5%.

The volume has decreased from 64 to 8 which is a decrease of 64 - 8 = 56.

56 / 64 = .875 * 100% = a decrease of 87.5% of the original volume.

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