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More Lessons for Grade 9

Math Worksheets

Examples, solutions, videos, worksheets, games, and activities to help Algebra students learn how to solve word problems that involve the volume of an open box.

**How to find the dimensions of a cardboard used to form a box given the volume of the box?**

Example:

The length of a piece of cardboard is five inches more than the width. The four corners are cut off so that the sides can be folded up to form a box. Each of the cut corners measures one and a half inches by one and a half inches, and the volume of the box is 189 cubic inches. What are the original dimensions of the piece of cardboard?**Volume Word Problems - Geometry Help**

Open box volume problem

Example:

An open box with a square base is to be made from a square piece of cardboard 36 inches on a side by cutting out a square from each corner and turning up the sides.

(a) Express the volume V of the box as a function of the length of the side of the square cut from each corner.

(b) What is the volume if a 7-inch square is cut out?

(c) What is the volume if a 16-inch square is cut out?

(d) Graph V(x). Choose the correct graph.

**Find width and length of open box given the volume**

Example:

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 3354 in^{3}, what were the original dimensions of the piece of metal?
**Volume of an Open Box**

This video will demonstrate how to calculate the maximum volume of an open box when congruent squares are removed from a rectangular sheet of cardboard. (We will use a graphing calculator and will not be using calculus)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 9

Math Worksheets

Examples, solutions, videos, worksheets, games, and activities to help Algebra students learn how to solve word problems that involve the volume of an open box.

Example:

The length of a piece of cardboard is five inches more than the width. The four corners are cut off so that the sides can be folded up to form a box. Each of the cut corners measures one and a half inches by one and a half inches, and the volume of the box is 189 cubic inches. What are the original dimensions of the piece of cardboard?

Open box volume problem

Example:

An open box with a square base is to be made from a square piece of cardboard 36 inches on a side by cutting out a square from each corner and turning up the sides.

(a) Express the volume V of the box as a function of the length of the side of the square cut from each corner.

(b) What is the volume if a 7-inch square is cut out?

(c) What is the volume if a 16-inch square is cut out?

(d) Graph V(x). Choose the correct graph.

Example:

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 3354 in

This video will demonstrate how to calculate the maximum volume of an open box when congruent squares are removed from a rectangular sheet of cardboard. (We will use a graphing calculator and will not be using calculus)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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