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: Multiply the three dimensions.

\[

$$\begin{align*} V&=\frac{3}{7}\times\frac{1}{5}\times\frac{7}{8}\\ &=\frac{3\times1\times7}{7\times5\times8}\\ &=\frac{3\times\cancel{7}}{\cancel{7}\times5\times8}\\ &=\frac{3}{5\times8}\\ &=\frac{3}{40} \end{align*}$$

\]

Answer:

The volume of the rectangular prism is \(\frac{3}{40}\) cubic centimeters.