SOLUTION: Anyone have any idea of how to solve this: The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surf

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Anyone have any idea of how to solve this: The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surf      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 228828: Anyone have any idea of how to solve this:
The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surface area is 54cm^2.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a cube with the side length x is V(x)=x^3.
Find the rate of change of volume with respect to the side length if the surface area is 54cm^2.
:
We know the surface area of a cube = 6x^2 (total area of the six sides)
6x^2 = 54
x^2 = 54%2F6
x^2 = 9
x = 3
:
Vol = x^2
V = 3^3
V = 27 cu/cm
:
We can say the relationship SA%2FVol = %286x%5E2%29%2Fx%5E3 = 6%2Fx (where x = 1 side)
:
:
See if this is true
Let v = 125 cu/cm
x^3 = 125
x = 3sqrt%28125%29
x = 5 cm
:
Find the surface area
SA = 6(5^2)
SA = 6(25)
SA = 150
:
150%2F125 = 6%2F5