SOLUTION: One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What

Question 193147: One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What is the volume of the cube?
Please explain how to solve this problem.
Found 2 solutions by Earlsdon, Alan3354:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the dimension of one side of the original cube. Its volume is
The three sides of the new solid are: x, (x-1), and (x+1).
The volume of the new solid is:

and this is said to be equal to five less than that of the cube, or , so....
Subtract from both sides.
or

The volume of the cube is then...
substitute x = 5.

cubic units.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What is the volume of the cube?
The volume of a cube (or rectangular solid) with sides a is
abc
V = a^3
V-5 = (a-1)*(a+1)*a
V-5 = a^3 - a
a^3 - 5 = a^3 - a
a = 5

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