Question

a rectangular prism has a length of 5 feet, a width of $3\frac{1}{2}$ feet, and a volume of $96\frac{1}{4}$ cubic feet. what is the height of the prism?

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular prism is $V = l\times w\times h$, where $V$ is volume, $l$ is length, $w$ is width and $h$ is height. We need to solve for $h$, so $h=\frac{V}{l\times w}$.

Step2: Convert mixed - numbers to improper fractions

$3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$ and $96\frac{1}{4}=\frac{96\times4+1}{4}=\frac{385}{4}$.

Step3: Substitute values into the formula

$h=\frac{\frac{385}{4}}{5\times\frac{7}{2}}$. First, calculate $5\times\frac{7}{2}=\frac{35}{2}$. Then $h = \frac{385}{4}\div\frac{35}{2}$.

Step4: Divide by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. So $h=\frac{385}{4}\times\frac{2}{35}=\frac{385\times2}{4\times35}=\frac{770}{140} = 5.5$.

Answer:

$5.5$