SOLUTION: 6 times the volume of a cube is equal to the sum of its surface area and the total length of its 12 edges. Find the dimensions of the cube. Please help me with this problem. I c

Question 724392: 6 times the volume of a cube is equal to the sum of its surface area and the total length of its 12 edges. Find the dimensions of the cube. Please help me with this problem. I can not figure it out and would greatly appriciate it!
Found 2 solutions by ankor@dixie-net.com, mananth:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
6 times the volume of a cube is equal to the sum of its surface area and the total length of its 12 edges. Find the dimensions of the cube.
:
let x = one side of the cube
then
6x^2 = the surface area
and
x^3 = the volume
and
12x = total length of the 12 edges
:
" 6 times the volume of a cube is equal to the sum of its surface area and the total length of its 12 edges. "
6x^3 = 6x^2 + 12x
simplify, divide by 6x
x^2 = x + 2
x^2 - x - 2 = 0
factors to
(x-2)(x+1) = 0
the positive solution
x = 2 cm is the side of the cube
:
:
You can confirm this in the original equation
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let side of cube be s
6 times volume of cube= 6s^3
surface area = 6s^2
length of 12 edges = 12s
6s^3= 6s^2+12s
divide by 6s
s^2=s+2
s^2-s-2=0
s^2+2s-s-2=0
s(s+2)-1(s+2)=0
(s+2)(s-1)=0
s=-2 or 1
ignore negative
side = 1 unit
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