Questions: Find the volume of the rectangular prism. Write your answer in simplest form.

Solution Steps

The volume 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.

In this case, we have:

$l = \frac{3}{4}$ yd $w = \frac{1}{7}$ yd $h = \frac{2}{5}$ yd

Substituting these values into the formula, we get:

$V = \frac{3}{4} \times \frac{1}{7} \times \frac{2}{5}$

Multiply the fractions:

$V = \frac{3 \times 1 \times 2}{4 \times 7 \times 5}$ $V = \frac{6}{140}$

The fraction $\frac{6}{140}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$V = \frac{6 \div 2}{140 \div 2}$ $V = \frac{3}{70}$

Final Answer: The volume of the rectangular prism is $\frac{3}{70}$ yd³