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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the dimension of one side of the original cube. Its volume is V%5Bc%5D+=+x%5E3
The three sides of the new solid are: x, (x-1), and (x+1).
The volume of the new solid is:
V%5Bn%5D+=+%28x%29%28x-1%29%28x%2B1%29
V%5Bn%5D+=+x%5E3-x and this is said to be equal to five less than that of the cube, or x%5E3-5, so....
x%5E3-x+=+x%5E3-5 Subtract x%5E3 from both sides.
-x+=+-5 or
x+=+5
The volume of the cube is then...
V%5Bc%5D+=+x%5E3 substitute x = 5.
V%5Bc%5D+=+5%5E3
highlight%28V%5Bc%5D+=+125%29 cubic units.

Answer by Alan3354(69443) About Me  (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