SOLUTION: A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 35¢/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 35¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top c      Log On


   

Question 1129931: A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 35¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 23¢/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 josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h, height
x, side length

hx%5E2=20
h=20%2Fx%5E2 
SURFACES    AREAS         PRICES     PARTIAL COSTS (cents)

BASE          x^2           35       35x^2

SIDES       4hx             10       10*4(20/x^2)x

TOP          x^2            23       23x^2

Simplifying the sum of costs for the cost function,
58x%5E2%2B800%2Fx cents