Geometry

On a rectangular piece of cardboard with perimeter 11 inches, three parallel and equally spaced creases are made. The cardboard is then folded along the creases to make a rectangular box with open ends. Letting x represent the distance (in inches) between the creases, use a graphing calculator to find the value of that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.

values of x that maximizes volume = in
Maximum volume= in^3

I'm so lost and don't know where to start any help would be greatly appreciated

  1. 👍
  2. 👎
  3. 👁
  1. This was answered by DrRuss on 1/21 at 6:39 am. I can't link so I pasted his answer below.

    I would start with a drawing as I do for most problems. Draw a reactangle 4x one side and b the other.

    The perimeter is then 4x+b+4x+b=11

    8x+2b=11

    if this is folded to a tube then the volume of the tube is bx^2, i.e. a tube with cross sectional area x^2 and length b.

    so V=bx^2

    rearrangen and substitute for b into the equation above gives

    8x+2V/(x^2) = 11

    or

    8x^3+2V=11x^2

    or

    V=5.5x^2-4x^3

    which you can plot to find max V

    I got 1.54 in^3 as the max volume

    but check the maths!

    1. 👍
    2. 👎
  2. Ok but I still don't know how to get the values of x that maximizes volume = in

    1. 👍
    2. 👎
  3. sorry, I didn't know that.

    you should have said that in your 1st post above. the tutors would see that this question was answered and refer you to the original answer.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. 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 in² and

  3. math

    a 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard.the sides are folded up to make an open box with a maximum volume.if the perimeter of the base is 50cm,what are the dimensions of the box.

  4. Math HELP!!

    Chuck needs to cut a piece of cardboard for an art project at school. He has four pieces of cardboard that he can cut from: 6 inches, 5 inches, 7 inches, and 3 inches. If the length of the cardboard he needs is √35 inches, which

  1. 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

  2. Math Please Help

    A pizza box top with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides. If the area of the base is to 144 in^2, what

  3. Calculus

    Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box

  4. Precalculus

    From a rectangular piece of cardboard having dimensions a × b, where a = 40 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the

  1. math

    A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 12 in. and L = 20

  2. Math

    A pizza box with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides (see the figure). If the area of the base is to be

  3. 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

  4. Pre-Alegebra

    3. If a number is not a rational number, then it is _____. (1 point) an integer an irrational number a whole number a radical*** 4.Mrs. Clarkson designed a rectangular garden with a length of 15 meters and a width of 8 meters. She

You can view more similar questions or ask a new question.