Algebra

An open box is to be constructed from a rectangular sheet of tin 3 meters wide by cutting out a 1-meter square from each corner and folding up the sides. The volume of the box is to be 2 cubic meters. What is the length of the tin rectangle?

  1. 👍 0
  2. 👎 0
  3. 👁 459
  1. V = area of base * height

    Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.

    So, the volume = width * height * length
    2 = 1 * 1 * length

    what, oh, what could be the length?
    2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.

    1. 👍 0
    2. 👎 0
  2. Draw a picture showing width = 3 and
    Draw the corner cutouts.
    Label the length of each edge
    If the total length of the sheet is X,
    Then, (X - 2)(1)(1) = 2 making X = 4 meters.

    1. 👍 0
    2. 👎 0
  3. V = area of base * height

    Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.

    So, the volume = width * height * length
    2 = 1 * 1 * length

    what, oh, what could be the length?
    2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.
    Algebra - tchrwill, Tuesday, October 4, 2011 at 10:40am

    Draw a picture showing width = 3 and
    Draw the corner cutouts.
    Label the length of each edge
    If the total length of the sheet is X,
    Then, (X - 2)(1)(1) = 2 making X = 4 meters.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize

  2. 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

  3. Calculus

    A rectangular tank with a square base, an open top, and a volume of 864 ft^3 is to be constructed of the sheet steel. Find the dimensions of the tank that minimize the surface area

  4. calculus

    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.

  1. Applied Calculus

    If an open box is made from a tin sheet 7 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two

  2. maths-urgently needed

    The volume of a cylinder is 48.125 cm3, which is formed by rolling a rectangular paper sheet along the length of the paper. If cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting

  3. Maths

    A cylindrical tin full of engine oil has a diameter of 12cm and a height of 14cm. The oil is poured into a rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin?

  4. maths

    An open rectangular box has internal dimensions 2m long, 20cm wide and 22.5cm deep. If the box is made of wood 2.5cm thick, calculate the volume of the wood in cm cube.

  1. calculus

    An open rectangular box having a volume of 256 is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x

  2. Math

    From an 8 inch by 10 inch rectangular sheet of paper, squares of equal size will be cut from each corner. The flaps will then be folded up to form an open-topped box. Find the maximum possible volume of the box.

  3. maths

    The rectangle box with square base is open at the top. The maximum volume of the box made from 1200 m2 tin,in m3 is:

  4. Math

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

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