PreCal

A square sheet of cardboard 18 inches is made into an open box (there is no top), by cutting squares of equal size out of each corner and folding up the sides. Find the dimensions of the box with the maximun volume.

Volume= base(width)height

but base + 2H =18
base + 2W=18

since squares are cut out of the corners, base and width are the same.

Volume=base^2 * height

but height= 9 - base/2
Volume = base^2 (9-base/2)

differentiate, set to zero, solve.

oooops you are in precal. If you don't know how to differentiat a uv function, then
graph this function for max volume.

x^4+6<5X^2

  1. 👍 0
  2. 👎 0
  3. 👁 345
asked by Chau

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    A square piece of cardboard, 24 inches by 24 inches, is to be made into an open box by cutting out each of the four corners. Each side of the box will then be folded up. Find the maximum volume that the box can hold.

    asked by Tom on November 13, 2014
  2. Geometry

    A box of cereal measures 8 inches high and 2 inches deep. If all surfaces are made of cardboard and the total amount of overlapping cardboard in the box is 7 square inches, how much cardboard is used to make the cereal box?

    asked by Sholanda on May 29, 2012
  3. Math

    Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

    asked by Jamie on June 23, 2009
  4. Math

    Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

    asked by Jacinta on June 25, 2009
  5. math

    A cardboard box is open at one end and is shaped like a square prism missing one of its square bases. The volume of the prism is 810 cubic inches, and its height is 10 inches. A)What is the length of each side of the base? B)Draw

    asked by kyle on April 28, 2015
  6. algebra

    Open-top box. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then

    asked by genevive on October 8, 2009
  7. calculus

    an open rectangular box is to be made from a piece of cardboard 8 inches wide and 8 inches long by cutting a square from each corner and bending up the sides. a. express the volume of the box as a function of the size x cutout

    asked by ashley on September 7, 2010
  8. calculus optimization problem

    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 30 inches long and 14 inches wide find the dimensions of the

    asked by sasha on April 3, 2013
  9. Maths- Calculus

    a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard

    asked by Daksh on August 3, 2013
  10. MATH

    An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square of side x inches from each corner and turning up the sides.Graph V=V(x)

    asked by lisa on April 18, 2014
  11. 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

    asked by Jim on March 7, 2012

More Similar Questions