SOLUTION: The edge of one cube is 4 cm longer than the edge of a second cube. The volumes of the cubes differ by 316cm^3. Find the length of the edge of each cube.

Question 1133400: The edge of one cube is 4 cm longer than the edge of a second cube. The volumes of the cubes differ by 316cm^3. Find the length of the edge of each cube.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
volume of a cube is edge^3 or x^3 for smaller cube
so (x+4)^3-x^3=316 cm^3. Using binomial expansion, or one can foil out (x+4)^2*(x+3)
x^3+12x^2+48x+64-x^3=316cm^3
12x^2+48x-252=0
divide by 12
x^2+4x-21=0
(x+7)(x-3)=0
x=3 cm smaller cube side length
x+4=7 cm larger cube side length
volumes are 343 cm^2 and 27 cm^3 or 316 cm^3 difference.

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