calculus

posted by .

You are planning to make an open-top box from an 12 in by 12 in piece of cardboard
by cutting congruent squares from the corners and folding up the sides.

What are the dimensions (of the 3 sides) of the largest volume you can make this way?

  • calculus -

    let the size of the cut out squares be x by x inches
    so the base of the box is 12-2x by 12-2x and its height is x inches.
    volume = x(12-2x^2

    expand, then find d(volume)dx
    set that equal to zero and solve for x,
    from which you can then find the dimensions

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. optimal dimensions

    Applications of derivatives You are planning to make an open rectangular box from an 8 by 15 inch piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest …
  2. math

    you want to make an open-topped box from a 20 cm by 20 cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. what are the dimensions of each square, to the nearest hundredth …
  3. math

    An open-topped box is made from a rectangular piece of cardboard, with dimensions of 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. Determine the dimensions of the squares to be cut to create …
  4. 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?
  5. math

    An open box is made from a rectangular piece of cardboard, with dimensions of 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. Determine the dimensions of the squares to be cut to create a box …
  6. math

    An open topped box can be created by cutting congruent squares from each of the 4 corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut …
  7. math grade 12

    A open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Derermine the dimensions of the square that must be cut …
  8. Math

    An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be …
  9. 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 …
  10. Calculus 1

    A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume …

More Similar Questions