SOLUTION: This word problem is kind of tough, I am trying to figure out how to do it so could you please help me figure it out? P.S- how do you find the volume of a cube? Question: The e

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Question 24342: This word problem is kind of tough, I am trying to figure out how to do it so could you please help me figure it out? P.S- how do you find the volume of a cube?
Question:
The edge of one cube is 4cm longer that the edge of a second cube. The volumes of the cubes differ by 316 cm2. Fid the length of each cube.

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Answer by AnlytcPhil(1806) About Me  (Show Source):
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This word problem is kind of tough, I am trying to figure out how to do it so
could you please help me figure it out? P.S- how do you find the volume of a
cube? 
Question:
The edge of one cube is 4cm longer that the edge of a second cube. The volumes
of the cubes differ by 316 cm3. Fid the length of each cube.

The formula for the volume of a cube is

     Volume = (edge)3  

That's why they call a number raised to the 3rd power the "CUBE" of the number,
for that's how you find the volume of a CUBE, by CUBING an edge!!!  

     Anyway, let each edge of the second smaller cube be x cm.

>>...The edge of one cube is 4cm longer that the edge of a second cube...<<

So each edge of the first (larger) cube is x+4 cm


                    _________
                   /  x+4   /|
  ______          /        / |
 /  x  /|        /________/  |
/_____/ |       |         |  |
| 2nd | |       |  1st    |  | 
|cube | /       |  cube   | /
|_____|/        |_________|/

V = x3            V = (x+4)3

>>...The volumes of the cubes differ by 316 cm3...<<

So 

      [Volume of 1st cube] MINUS [Volume of 2nd cube] = 316 c3

               (x+4)3        -          x3            = 316

                                                (x+4)3 - x3 = 316            
Write 1st term as 3 factors:
                                       (x+4)(x+4)(x+4) - x3 = 316
FOIL out the first two:
                                     (x2+4x+4x+16)(x+4) - x3 = 316
Combine middle two terms:
                                        (x2+8x+16)(x+4) - x3 = 316
Multiply each term in 1st
parentheses by each term is 2nd:  x3+4x2+8x2+32x+16x+64 - x3 = 316

Combine like terms:                      x3+12x2+48x+64 - x3 = 316

x3 and -x3 cancel out                            12x2+48x+64 = 316

Subtract 316 from both sides
to get 0 on the right                          12x2+48x-252 = 0    

Factor out 12                                  12(x2+4x-21) = 0

Factor the trinomial                           12(x+7)(x-3) = 0

Set each factor with a variable = 0         
Set first factor with a variable = 0            x+7 = 0                       
                                                  x = -7

Set first factor with a variable = 0            x-3 = 0                       
                                                  x = 3

Discard the negative answer.  Answer: smaller cube has edge = 3cm.
                                      larger cube has edge 3+4 or 7 cm.  
Edwin
AnlytcPhil@aol.com