Word Problems Involving Volume of Cubes and Rectangular Prisms

A step-by-step guide to using a table to write down a two-variable equation

here’s a step-by-step guide to solving word problems involving volume of cubes and rectangular prisms:

1. Read the problem carefully: Make sure you understand the information provided in the problem and what is being asked of you.
2. Identify the dimensions of the cube or rectangular prism: Look for the measurements of the length, width, and height of the object. Make sure you identify which dimension corresponds to which measurement.
3. Calculate the volume: Once you have identified the dimensions of the object, use the formula for finding the volume of a cube or rectangular prism, depending on the shape of the object. The formula for the volume of a cube is \(V = s^3\), where s is the length of one side of the cube. The formula for the volume of a rectangular prism is \(V = lwh\), where l is the length, w is the width, and h is the height of the rectangular prism. Substitute the appropriate values into the formula to calculate the volume.
4. Check your units: Make sure that the units of measurement used in the problem are consistent with the units used in the formula for finding the volume. If not, convert the units as necessary.
5. Round your answer: Round your answer to the appropriate number of significant figures, as specified in the problem.
6. Interpret your answer: Make sure you answer the question that is being asked in the problem. For example, if the problem asks for the volume of a rectangular prism in cubic inches, make sure your answer is expressed in cubic inches.
7. Check your work: Double-check your calculations to make sure you have not made any errors.

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It’s always a good idea to practice with a variety of problems to become comfortable with these steps.

Word Problems Involving Volume of Cubes and Rectangular Prisms – Example 1

Emma has a rectangular prism box for packing birthday presents that has a volume of 16600 cubic centimeters. The prism has a width of 28 centimeters and a height of 17 centimeters. What is the length of the box?
Solution:
To find out the length of the present box:
Step 1: Multiply the width by height. \(28×17=476\)
Step 2: Divide 16600 by 476 to find the length of the box.
\(16600÷476=35\)
So, the length is 35 cm.

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Word Problems Involving Volume of Cubes and Rectangular Prisms – Example 2

Luci bought a handmade rug for her mother’s birthday party. She returned home with a box that was 32 inches long, 24 inches wide, and 9 inches tall. What is the volume of the box?
Solution:
To find out the volume of the box (V), use the formula for the volume of a rectangular prism. \(V=lwh\).
\(32×24×9=6912 in^3\)
So, the area of the box is \(6912 in^3\).