SOLUTION: each edge of a cube is 2 cm longer than each edge of another cube. the volumes of the cubes differ by 98 cm cubed. can you find the lengths of the edges of each cube?

Question 538762: each edge of a cube is 2 cm longer than each edge of another cube. the volumes of the cubes differ by 98 cm cubed. can you find the lengths of the edges of each cube?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
each edge of a cube is 2 cm longer than each edge of another cube. the volumes of the cubes differ by 98 cm cubed.
can you find the lengths of the edges of each cube?
:
x = the edge of the smaller cube
then
x^3 = the volume
:
(x+2) = edge of the larger cube
then
(x+2)^3 = the volume
(x+2)*(x+2)*(x+2) = x^3 + 6x^2 + 12x + 8
:
Larger - smaller = 98 cub/cm
x^3 + 6x^2 + 12x + 8 - x^3 = 98
x^3 - x^3 + 6x^2 + 12x + 8 - 98 = 0
6x^2 + 12x - 90 = 0
simplify, divide by 6, results:
x^2 + 2x - 15 = 0
factors to
(x+5)(x-3) = 0
the positive solution
x = 3 cm is the length of the side of the small cube
then
5 cm is the length of the larger cube
:
:
Check this
5^3 = 125 cu/cm
3^2 = 27 cu/cm
----------------
diff: 98 cu/cm
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