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 \( V = l \times w \times h \).

Step2: Identify the length, width, and height

From the diagram, the length \( l=\frac{3}{7} \) cm, the width \( w = \frac{1}{5} \) cm, and the height \( h=\frac{7}{8} \) cm.

Step3: Substitute the values into the formula

\[
V=\frac{3}{7}\times\frac{1}{5}\times\frac{7}{8}
\]

Step4: Simplify the expression

First, notice that the \( 7 \) in the numerator of the third fraction and the \( 7 \) in the denominator of the first fraction can be canceled out:
\[
V=\frac{3}{\cancel{7}}\times\frac{1}{5}\times\frac{\cancel{7}}{8}=\frac{3\times1\times1}{1\times5\times8}=\frac{3}{40}
\]

Answer:

\(\frac{3}{40}\)