Question

geometry the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$, is $v = lwh$. find the height in inches of a rectangular prism with volume $6\text{ ft}^3$, width $12\text{ in.}$, and length $24\text{ in.}$

Explanation:

Step1: Convert volume unit

Since \(1\ ft = 12\ in\), then \(1\ ft^{3}=(12)^{3}\ in^{3}=1728\ in^{3}\).
The volume \(V = 6\ ft^{3}\), so \(V=6\times1728\ in^{3}=10368\ in^{3}\).

Step2: Solve for height \(h\)

Given \(V = lwh\), we can express \(h=\frac{V}{lw}\).
Substitute \(V = 10368\ in^{3}\), \(l = 24\ in\), \(w = 12\ in\) into the formula:
\(h=\frac{10368}{24\times12}\)
First calculate \(24\times12 = 288\).
Then \(h=\frac{10368}{288}=36\)

Answer:

\(36\) inches