How to find the volume of a prism

Lesson Procedure: Finding the Volume of a Right Rectangular Prism

Rectangular Prism

Look at the right rectangular prism on the right. The measurement of the length is 2¼ inches. The measurement of the width is 1/2 inch. The measurement of the height is 1 inch.

Change the dimensions of the right rectangular prism to improper-like fractions. The dimensions are 9/4, 2/4, and 4/4 inches.

To find the volume of this right rectangular prism, fill it with ¼ inch cubes. It takes 64 – ¼ inch cubes to fill one unit cube.

The right rectangular prism can be filled with ¼ inch cubes. It takes 9 x 2 x 4 cubes to fill this right rectangular prism. It takes 72 – ¼ inch cubes to fill this right rectangular prism.

The volume of the right rectangular prism is 9/4 x 2/4 x 4/4 = 72/64 or 1 8/64 or 1 1/8 cubic inches.

Individual or Group Work:

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Look at the right rectangular prisms below. Fill the prisms with unit cubes of the appropriate unit fraction edge lengths.

1. The measurement of the length is 2 inches. The measurement of the width is 1 inch. The measurement of the height is 3¾ inches. How many cubes with side lengths of ¼ would be needed to fill the prism? What is the volume of the prism? Show how you found your answers.

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2. The measurement of the length is 1½ inches. The measurement of the width is ½ inch. The measurement of the height is 4 inches. How many cubes with side lengths of 1/2 inch would be needed to fill the prism? What is the volume of the prism? Show how you found your answers.

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3. The measurement of the length is 4 1/2 inches. The measurement of the width is 1 ½ inch. The measurement of the height is 2 inches. How many cubes with side lengths of 1/2 inch would be needed to fill the prism? What is the volume of the prism? Show how you found your answers.

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4. The measurement of the length is 3/4 inches. The measurement of the width is ½ inch. The measurement of the height is 2 inches. How many cubes with side lengths of 1/4 inch would be needed to fill the prism? What is the volume of the prism? Show how you found your answers.

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5. The measurement of the length is 2½ inches. The measurement of the width is 3 ½ inch. The measurement of the height is 4 inches. How many cubes with side lengths of 1/2 inch would be needed to fill the prism? What is the volume of the prism? Show how you found your answers.

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