SOLUTION: A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the surface area A of the box in terms of the width w of the base. If

Algebra ->  Rectangles -> SOLUTION: A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the surface area A of the box in terms of the width w of the base. If      Log On


   

Question 1139273: A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the surface area A of the box in terms of the width w of the base. If the material for the base and top costs 20 dollars/ft2 and that for the sides costs 30 dollars/ft2 express the total cost C as a function of the width.
1a. A(w)=?ft^2
1b. C(w)=$
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = the height of the box
+V+=+w%5E2%2Ah+
+2+=+w%5E2%2Ah+
+h+=+2%2Fw%5E2+
-------------------
+A+=+2%2Aw%5E2+%2B+4%2Aw%2Ah+
+A+=+2%2Aw%5E2+%2B+4%2Aw%2A%28+2%2Fw%5E2+%29+
+A%28w%29+=+2%2Aw%5E2+%2B+8%2Fw+
-------------------------------------
+C%28w%29+=+20%2A%28+2%2Aw%5E2+%29+%2B+30%2A%28+8%2Fw+%29+
+C%28w%29+=+40w%5E2+%2B+240%2Fw+