Question

find the volume of the rectangular prism. write your answer in simplest form.

Explanation:

Step1: Recall the formula for the volume of a rectangular prism

The volume \( V \) of a rectangular prism is given by the product of its length \( l \), width \( w \), and height \( h \), so \( V = l \times w \times h \).
Here, \( l=\frac{4}{7}\) ft, \( w = \frac{1}{3}\) ft, and \( h=\frac{3}{5}\) ft.

Step2: Substitute the values into the formula

\( V=\frac{4}{7}\times\frac{1}{3}\times\frac{3}{5} \)

Step3: Simplify the expression

First, notice that \( \frac{1}{3}\times\frac{3}{5}=\frac{1\times3}{3\times5}=\frac{1}{5} \) (the 3 in the numerator and denominator cancels out).
Then, multiply this result by \( \frac{4}{7} \): \( V = \frac{4}{7}\times\frac{1}{5}=\frac{4\times1}{7\times5}=\frac{4}{35} \)

Answer:

\(\frac{4}{35}\) cubic feet