What is the volume of a rectangular prism that is 8.5 inches long, 3.25 inches wide, and 2 inches high?
Understand the Problem
The question is asking for the volume of a rectangular prism with given length, width, and height. We can find the volume by multiplying these three dimensions together.
Answer
$55\frac{1}{4}$ cubic inches.
Answer for screen readers
The volume of the rectangular prism is $55\frac{1}{4}$ cubic inches.
Steps to Solve
- Convert mixed numbers to improper fractions
Convert the length, width, and height from mixed numbers to improper fractions. This makes multiplication easier. $$ 8\frac{1}{2} = \frac{8 \cdot 2 + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2} $$ $$ 3\frac{1}{4} = \frac{3 \cdot 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} $$ The height is already a whole number, 2.
- Write out the formula to calculate the volume of the prism
The volume $V$ of a rectangular prism is given by the formula: $$ V = l \cdot w \cdot h $$ where $l$ is the length, $w$ is the width, and $h$ is the height.
- Substitute the values into the volume formula
Substitute the given values (as improper fractions) into the formula: $$ V = \frac{17}{2} \cdot \frac{13}{4} \cdot 2 $$
- Simplify and calculate the volume
Simplify by canceling the 2 in the numerator and denominator: $$ V = \frac{17}{1} \cdot \frac{13}{4} \cdot 1 = \frac{17 \cdot 13}{4} = \frac{221}{4} $$ Now, convert the improper fraction to a mixed number: $$ \frac{221}{4} = 55\frac{1}{4} $$
The volume of the rectangular prism is $55\frac{1}{4}$ cubic inches.
More Information
The volume is expressed in cubic inches since we are multiplying three lengths (each in inches) together.
Tips
A common mistake is to multiply the mixed numbers directly without converting them to improper fractions first. This can lead to incorrect results. Another error is to incorrectly convert mixed numbers to improper fractions, for example, by adding instead of multiplying. Finally, not simplifying the fraction to its lowest terms after multiplying can also be considered a mistake; although $\frac{221}{4}$ is equivalent to $55\frac{1}{4}$, the mixed number format is easier to grasp.
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