pre-calc

posted by moshie

A box with an open top is to be constructed by cutting equal-sized squares out of the corners of a 18 inch by 30 inch piece of cardboard and folding up the sides.


a) Let w be the length of the sides of the cut out squares. Determine a function V that describes the volume of the finished box in terms of w.
V(w) =

b) What width w would maximize the volume of the box?
w = inches

c) What is the maximum volume?
V = cubic inches

  1. Steve

    V(w) = (18-2w)(30-2w)

    max V where dV/dw = 0

  2. Steve

    Oops. base * height is volume

    V(w) = (18-2w)(30-2w)w

  3. Anonymous

    gfg

Respond to this Question

First Name

Your Answer

Similar Questions

  1. algebra

    Open-top box. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what …
  2. calculus

    An open box is to be made out of a 8-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Dimensions …
  3. Calculus

    An open top box is made by cutting congruent squares from the corners of a 12 inch by 9 inch sheet of cardboard and then folding the sides up to create the box. What are the dimensions of the box which contains the largest volume?
  4. Math

    An open box is to be made from a 11 inch by 11 inch piece of cardboad. this box is constructed by cutting squares that measure x inches on each side from the corners of the cardboard and turning up the sides. Use a graphical calculator …
  5. Algebra

    A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding …
  6. College Math

    An open-topped rectangular box is to be constructed from a 24 inch by 36 inch piece of cardboard by cutting out squares of equal sides from the corners and then folding up the sides. What size squares should be cut out of each of the …
  7. Math

    A box with a rectangular base and no top is to be made from a 9 inch by 12 inch piece of cardboard by cutting squares out of the corners and folding up the sides. What size (side-length) squares should be cut out to make the box have …
  8. Calc

    An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Dimensions …
  9. calculus

    An open box is to be made out of a 10-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
  10. Pre-algebra

    Hey I'm having a lot of trouble with this question. An open box is to be made from a 20 inch by 40 inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. A) What size should the …

More Similar Questions