Purchase Solution

Maximizing the Volume of an Open-Top Box

Not what you're looking for?

Ask Custom Question

An open top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.

Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and also graph this function.

Using the graph what is the value of x that will produce the maximum volume?

Purchase this Solution
Solution Summary

This solution provides a detailed response, which illustrates how to calculate the volume of an open-top box. The solution is easy to follow and includes a graph, which is attached in an accompanying Word document as part of this solution.

Solution Preview

After cutting four squares, the length that is left is 8-2x feet and the width that is ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Maximizing Volume of an Open Top Box by Graphing

    The volume of an open-top box is found by graphing.

  • Maximizing the Volume of an Open Top Box

    120817 Maximizing the Volume of an Open Top Box 1.You are to design a container box by cutting out the four corners of a square cardboard sheet that is 1600 cm2 in area. The box must have a square base and an open top.

  • Maximizing the Volume of an Open Top Box

    166773 Maximizing the Volume of an Open Top Box The total surface area of a square based open-top rectangular box is 12 cm^2. Find the dimensions of the box of maximum volume. Suppose the base of the box is x cm and the height is y cm.

  • Maximizing the Volume of an Open Top Box

    139456 Maximizing the Volume of an Open Top Box.. A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open-top box.

  • Mean Value Theorem and Maximizing Volume of an Open Box

    109699 Mean Value Theorem and Maximizing Volume of an Open Box The width of an open box is half its height and its surface area is 75 cm3. Find the dimensions to maximize its volume.

  • Maximizing the Volume of a Rectangular Box

    181690 Maximizing the Volume of a Rectangular Box You are planning to make an open rectangular box from a 12-by 14-cm piece of cardboard by cutting congruent squares from the corners and folding up the sides.

  • Maximum Volume of an Open-Top Box

    139474 Maximum Volume of an Open-Top Box A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open top box.

  • Maximum Volume of an Open Top Box

    86275 Maximum Volume of an Open-Top Box An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps.

  • volume of an open-top box

    86917 Volume of open top box An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps.

View More Related Solutions