Question

an aquarium can be modeled as a right rectangular prism and it can hold 1368 cubic inches of water when it is full. its length is 19 in and width is 9 in. find the height of the aquarium in inches. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the volume formula for a right rectangular prism

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

Step2: Substitute the known values into the formula

We know that \(V = 1368\) cubic inches, \(l = 19\) inches, and \(w = 9\) inches. Substituting these values into the formula \(V=l\times w\times h\), we get \(1368=19\times9\times h\).
First, calculate \(19\times9 = 171\). So the equation becomes \(1368 = 171\times h\).

Step3: Solve for \(h\)

To find \(h\), we use the formula \(h=\frac{V}{l\times w}\). Since \(V = 1368\) and \(l\times w=171\), then \(h=\frac{1368}{171}\).
\(h = 8\) inches.

Answer:

\(8\) inches