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 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.

Step2: Substitute the given values into the formula

Here, \( l = \frac{2}{5}\text{ cm}\), \( w=\frac{4}{9}\text{ cm}\), and \( h=\frac{3}{5}\text{ cm}\). So \( V=\frac{2}{5}\times\frac{4}{9}\times\frac{3}{5}\).

Step3: Multiply the fractions

First, multiply \( \frac{2}{5}\times\frac{4}{9}=\frac{2\times4}{5\times9}=\frac{8}{45}\). Then multiply \( \frac{8}{45}\times\frac{3}{5}\). Using the rule \( \frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\), we have \( \frac{8\times3}{45\times5}=\frac{24}{225}\). Simplify \( \frac{24}{225}\) by dividing both the numerator and denominator by 3. \( \frac{24\div3}{225\div3}=\frac{8}{75}\).

Answer:

\(\frac{8}{75}\text{ cm}^3\)