Question

a rectangular prism is 18 inches long, 6\frac{1}{2} inches wide, and has a volume of 292\frac{1}{2} cubic inches. which equation can you use to find the height of the prism, h? 292\frac{1}{2}=18\cdot6\frac{1}{2}\cdot h 18\cdot6\frac{1}{2}=292\frac{1}{2}\cdot h what is the height of the prism? inches

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. Given $l = 18$, $w=6\frac{1}{2}=\frac{13}{2}$ and $V = 292\frac{1}{2}=\frac{585}{2}$. Substituting these values into the formula gives $\frac{585}{2}=18\times\frac{13}{2}\times h$, or $292\frac{1}{2}=18\times6\frac{1}{2}\times h$.

Step2: Solve for $h$

We have the equation $292\frac{1}{2}=18\times6\frac{1}{2}\times h$. First, calculate $18\times6\frac{1}{2}=18\times\frac{13}{2}=117$. So the equation becomes $\frac{585}{2}=117h$. Then $h=\frac{585}{2}\div117=\frac{585}{2}\times\frac{1}{117}=\frac{5}{2} = 2.5$.

Answer:

1. First - part answer: $292\frac{1}{2}=18\times6\frac{1}{2}\times h$
2. Second - part answer: $2.5$