SOLUTION: A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top c

Algebra ->  Rectangles -> SOLUTION: A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top c      Log On


   

Question 840764: A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 32¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 32¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
:
The height
h = 20%2Fx%5E2
:
The base
.40x^2
The 4 sides
4(.10*x*20%2Fx%5E2) = 4(.10*20%2Fx) = 8%2Fx
The top
.32x^2
Total cost
c(x) = .4x^2 + .32x^2 + 8%2Fx
c(x) = .72x^2 + 8%2Fx
:
:
This is one of those problems I am not 100% sure about, if I screwed it up,
would appreciate if you let me know. Where I screwed it up would be nice too.
email me: ankor@att.net