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Joan has a piece of construction paper 22in long by 16in wide. She cuts a 2in by 2in square from each conner. She then folds up the sides of the paper and forms a box with an open top. What is the volume of the box and how do you figure it?

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Mar 11, 2011
Math Volume Problem
by: Staff


The question:

Joan has a piece of construction paper 22in long by 16in wide. She cuts a 2in by 2in square from each conner. She then folds up the sides of the paper and forms a box with an open top. What is the volume of the box and how do you figure it?



The answer:

The volume of the open top box depends on its final dimensions.

Volume = length * width * height


Drawing a diagram is the easiest way to visualize the dimensions of the box.


Step 1: Using a piece of graph paper, draw a diagram of the construction paper (22 inches by 16 inches) to scale.

Click the link below to see a diagram of the construction paper.

http://www.solving-math-problems.com/images/box-volume-01-blank-construction-paper.png


Step 2: Mark two inch squares at each corner of the construction paper which is shown on the diagram.

Click the link below to see a how the diagram should look.

http://www.solving-math-problems.com/images/box-volume-02-mark-2-in-corner-squares.png


Step 3: Erase the two inch squares at each corner of the diagram.

Click the link below to see a how the diagram should look.

http://www.solving-math-problems.com/images/box-volume-03-erase-2-in-corner-squares.png


Step 4: Mark the fold lines on the diagram.

Click the link below to see a how the diagram should look.

http://www.solving-math-problems.com/images/box-volume-04-mark-fold-lines.png


Step 5: At this point, cut the diagram out, and fold along the dotted lines to create the box.

Click the link below to see what the box should look like.

http://www.solving-math-problems.com/images/box-volume-05-final-box.png


Computing the volume:

The final dimensions of the box are:

Length: 18 inches
Width: 12 inches
Height: 2 inches

Volume of Box = length * width * height

Volume of Box = (18 inches) * (12 inches) * (2 inches)

Volume of Box = 432 cubic inches



The final answer is: 432 cubic inches



Thanks for writing.


Staff
www.solving-math-problems.com


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