Math

A 5 cm by 5 cm 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 50 cm, what are the dimensions of the box?

  1. 👍 0
  2. 👎 0
  3. 👁 79
asked by Anonymous

  1. If the cardboard had dimensions x and y, then
    2(x-10 + y-10) = 50
    x+y = 45
    Now, the volume is
    v = 5(x-10)(y-10) = 5(x-10)(35-x) = -5(x^2-45x+350)
    The vertex of this parabola (maximum volume) is at (45/2 , 3125/4)

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A Candy box is made from a piece of cardboard that meaasures 11 by 7 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from

    asked by Anonymous on April 27, 2011

  2. geom/trig

    Using scissors to cut a rectangular piece of paper from one corner ro the opposite corner. The cut is 36 cm long and makes a 34 degree angle to the uncut edge. How many cm long is the paper (from the corner where he started the

    asked by lola on January 16, 2012

  3. 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

    asked by Mishaka on December 16, 2011

  4. algebra

    A rectangular piece of cardboard is 2 units longer than it is wide? From each of its corner a square piece 2 units on a side is cut out.The flaps are then turned up to form an open box that has a volume of 70 cubic units.Find the

    asked by Firdous on April 29, 2013

  5. 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

    asked by Anonymous on August 26, 2015

  6. Math

    You want to create an open rectangular box from a rectangular box. from a square piece of cardboard 20 inches by 20 inches. You will cut a 3 inch square from each corner. Draw a diagram and find the length of the box. Can someone

    asked by Olivia on August 24, 2014

  7. Calculus- PLEASE HELP

    A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the

    asked by James on June 14, 2016

  8. math 12

    $identical\:squares\:are\:cut\:from\:each\:corner\:of\:a\:rectangular\:piece\:of\:cardboard,\:7\:cm\:by\:10\:cm.\:The\:sides\:are\:then\:folded\:up\:to\:make\:a\:box\:with\:an\:open\:top.\:If\:the\:volume\:of\:the\:box\:is\:25\:cubic\:centimeter,\:how\:long\:is\:the\:side\:of\:each\:square?$

    asked by sally on September 10, 2014

  9. Calculus

    A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the

    asked by James on June 13, 2016

  10. math

    Identical square are cut from each corner of an 8 inch by 11.75inch rectangular piececof cardboard.the sides are folded up to make a box with no top . if the volume of the resulting box is 63.75 cubic inches how long is the edge

    asked by zoren on August 11, 2016

More Similar Questions