Question

volume of rectangular prisms
v = l×w×h
v = b×h
find the volume of the rectangular prism. enter your answer in simplest form.
diagram of a rectangular prism with dimensions \\(\frac{1}{2}\\) ft, \\(\frac{3}{4}\\) ft, and \\(3\frac{1}{4}\\) ft

Explanation:

Step1: Identify the formula for the volume of a rectangular prism.

The formula for the volume \( V \) of a rectangular prism is \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height. From the diagram, we can identify the dimensions: \( l = 3\frac{1}{4} \) ft, \( w = \frac{3}{4} \) ft, and \( h = \frac{1}{2} \) ft.

Step2: Convert the mixed number to an improper fraction.

First, convert \( 3\frac{1}{4} \) to an improper fraction. \( 3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \).

Step3: Multiply the three dimensions together.

Now, we multiply \( l \), \( w \), and \( h \):
\[
V = \frac{13}{4} \times \frac{3}{4} \times \frac{1}{2}
\]
First, multiply the numerators: \( 13 \times 3 \times 1 = 39 \).
Then, multiply the denominators: \( 4 \times 4 \times 2 = 32 \).
So, \( V = \frac{39}{32} \).

Step4: Convert the improper fraction to a mixed number (if needed).

\( \frac{39}{32} = 1\frac{7}{32} \).

Answer:

The volume of the rectangular prism is \( \frac{39}{32} \) (or \( 1\frac{7}{32} \)) cubic feet.