Math

An open gift box is to be made from a square piece of material by cutting four-centimeter squares from each corner and turning up the sides (see figure). The volume of the finished gift box is to be 324 cubic centimeters. Find the size of the original piece of material.

  1. 👍
  2. 👎
  3. 👁
  1. height = 4 cm
    length = width = x-8

    (x-8)(x-8)4 = 324
    x^2 -16 x + 64 = 81

    x^2 - 16 x - 17 = 0

    (x-17)(x+1) = 0
    well it is not -1 so
    x = 17
    17 by 17

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    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.

  2. 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

  3. 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? what is the

  4. Math

    AN OPEN BOX IS TO BE MADE FROM A CARDBOARD 20 INCHES BY 14 INCHES, BY CUTTING A SQUARE FROM EACH CORNER AND FOLDING UP THE SIDES. FIND THE DIMENSIONS OF THE BOX THAT WILL MAXIMIZE THE VOLUME OF THE BOX

  1. 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

  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

  3. college algebra

    An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the

  4. Calculus (Optimization)

    A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a small square from each corner and bending up the sides. What size square should be cut from each corner for the box to have

  1. Pre Cal 12

    A 12cm by 8cm rectangular piece of metal is to be made into an open-top box by cutting a sqaure from corner and folding up the resulting flaps (sides). If the volume of the lidless box is 36 cm what are the integer dimensions of

  2. math

    a box is to be made by cutting out the corners of a square piece of cardboard and folding the edges up. if 3-inch squares are to be cut out of the corners and the box contains 243 cubic inches, what is the length of a side of the

  3. 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.

  4. math

    An open box is to be made from a flat square piece of material 20 inches in length and width by cutting equal squares of length x from the corners and folding up the sides. (a) Write the volume V of the box as a function of x.

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