Calculus

posted by Alexa

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.

  1. Steve

    if the squares are of side x, then

    v = x(12-2x)^2 = 4x^3-48x^2+144x
    dv/dx = 12x^2 - 96x + 144
    = 12(x-2)(x-6)

    so, v has a max at x=2.

  2. Alexa

    Thank you sir.

  3. Joey

    A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with
    side length x from each corner and folding up the sides.

    a. Find a formula for the volume of the box in terms of x

    b. Find the value for x that will maximize the volume of the box. Round to 2 decimal places if needed.

  4. Kana

    v=(13-2x)(11-2x).x

    dV/dx= 3x^2-96x+143

    use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a

    ans x=2.26

  5. Kana

    v=(13-2x)(11-2x).x

    dV/dx= 3x^2-96x+143

    use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a

    ans x=1.98

    sorry for the previous ans

Respond to this Question

First Name

Your Answer

Similar Questions

  1. calculus

    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 …
  2. Calculus

    an open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning up the sides. If the piece of cardboard is 12 cm by 24 cm, what are the dimensions of the box that has the largest volume …
  3. math

    A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 40 cm by 60 cm by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the …
  4. calculus

    7. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 40 cm by 60 cm by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the …
  5. 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 …
  6. 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 …
  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. 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. 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