calc

posted by .

by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the dimensions of the box that will yield the max volume. what is the max volume?

  • calc -

    let each side of the square to be cut out be x inches
    length of base = 16-2x
    width of base = 10-2x
    height of box = x inches

    V = x(16-2x)(10-2x) , where 0 < x < 5

    I would now expand that to get a cubic
    take the derivative, which is a quadratic,
    set the derivative equal to zero and solve for x

    Very straight forward question, most Calculus texts use that question as an introduction to optimization.

  • Precalc -

    Two Congruent squares are removed from one end of a rectangle 10 inch by 20 inch piece of cardboard. Two congruent rectangles are removed from the other end Determine the value of x so that the resulting box has maximum volume

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    a rectangular piece of cardboard that measures 4 by 3 inches is to be formed into a rectangular box by cutting squares with length x from each corner and folding up sides. Find the volumes of the box in terms of x
  2. math

    a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard. …
  3. math

    By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions of the box that …
  4. calculus

    By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 14 in. long and 6 in. wide, find the dimensions of the box that …
  5. calculus optimization problem

    by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 30 inches long and 14 inches wide find the dimensions of the box …
  6. 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 …
  7. Calculus

    By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 10 in. wide, find the dimensions of the box that …
  8. Math

    A box with an open top is to be made by cutting 5-inch squares from the corners of a rectangular piece of cardboard whose length is twice its width and then folding up the remaining flaps. Let x represent the width of the original …
  9. Math

    a rectangular piece of cardboard is twice as long as it is wide . from each of its for corners, a square piece 3 inches on a side cut out. the flaps at each corner are then turned up to form an open box. if the volume of the box is …
  10. math

    an open rectangular box is to be formed by cutting identical squares, each of side 2 in, one from each corner of a rectangular piece of cardboard, and then turning up the ends. If the area of the piece of cardboard is 160 inĀ² and …

More Similar Questions