calculus

posted by .

An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

  • calculus -

    Let x be the length of the side of the square taken off each corner. The open box will have length 56-2x, width 21-2x and height x.

    The volume of the box is
    V(x) = x(56-2x)(21-2x)

    Set the derivative dV/dx equal to zero and compute the corresponding x. Use that to compute the maximum volume.

    Someone will gladly critique your work if you show what you did and need additional assistance.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    open top rectangular box made from 35 x 35 inch piece of sheet metal by cutting out equal size squares from the corners and folding up the sides. what size squares should be removed to produce box with maximum volume.
  2. calculus

    an open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bending up the sides. what size should be cut out to create a box with the greatest volume?
  3. Math

    An open box is to be made from a 10-ft by 14-ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and folding up the sides. what size squares should be cut to obtain a box with largest possible …
  4. 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 …
  5. 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 …
  6. Calculas

    an open box is to be made from a square piece of cardboard whose sides are 19 inches long,by cutting squares of equal size from the corners and bending up the sides. Determine the size of the aquare that is to be cut out so that the …
  7. 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 …
  8. 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.
  9. 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 …
  10. Calculus

    What is the maximum volume in cubic inches of an open box to be made from a 16 in by 30 in piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides?

More Similar Questions