Question

find the volume of the rectangular prism. write your answer in simplest form. the rectangular prism has dimensions \\(\frac{3}{7}\\) yd, \\(\frac{2}{3}\\) yd, \\(\frac{5}{7}\\) yd.

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Identify the length, width, and height from the diagram

From the diagram, we have:

• Length \( l = \frac{5}{7} \) yd
• Width \( w = \frac{2}{3} \) yd
• Height \( h = \frac{3}{7} \) yd

Step3: Substitute the values into the volume formula

Substitute \( l = \frac{5}{7} \), \( w = \frac{2}{3} \), and \( h = \frac{3}{7} \) into the formula \( V = l \times w \times h \):

$$ V=\frac{5}{7}\times\frac{2}{3}\times\frac{3}{7} $$

Step4: Simplify the expression

First, notice that \( \frac{2}{3} \) and \( \frac{3}{7} \) have a common factor of 3 in the numerator and denominator. We can cancel out the 3:

$$ V=\frac{5}{7}\times\frac{2}{\cancel{3}}\times\frac{\cancel{3}}{7} $$

After canceling, we have:

$$ V=\frac{5}{7}\times\frac{2}{7} $$

Now, multiply the numerators and the denominators:

$$ V = \frac{5\times2}{7\times7}=\frac{10}{49} $$

Answer:

The volume of the rectangular prism is \(\frac{10}{49}\) cubic yards.