calculus

posted by .

An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box.
(a) Express the volume V of the box as a function of x, where x is edge length of the square cut-outs.
(b) What are the dimensions of the box that enclose the largest possible volume? State your answer in the form length by width by height.
(c) What is the maximum volume?

  • calculus -

    let each side of the equal squares be x inches
    length of box = 24-2x
    width of box = 24-2x
    height of box = x

    a) Volume = x(24-2x)(24-2x)

    b) expand the volume equation, then take the first derivative.
    Set that derivative equal to zero. You will have a quadratic equation. Take the positive answer which lies between 0 and 12

    c) put the answer from b) into the volume equation and evaluate.

  • calculus -

    20>o

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, …
  2. Calculus

    A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must …
  3. calculus

    An Open Box Of Maximum Volume Is To Be Made From A Square Piece Of Cardboard Twentyfour Inches On Each Side By Cutting Equal Suares Frm The Corners And Turning Up The Sides
  4. college algebra

    An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the square …
  5. Math

    A cardboard manufacturer wishes to make open boxes from square pieces of cardboard of side 12 in. by cutting equal squares from the four corners and turning up the sides. Let x inches be the length of the side of the the square to …
  6. 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 …
  7. Engineering

    A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 in on the side, find the size of the squares that must …
  8. Mathematics

    An open box is made from a square piece of sheet metal 19 inches on a side by cutting identical squares from the corners and turning up the sides. Express the volume of the box, V, as a function of the length of the side of the square …
  9. Calculus

    An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.
  10. Math

    An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made. Help!

More Similar Questions