Question

an aquarium can be modeled as a right rectangular prism and it can hold 312 cubic inches of water when it is full. its length is 13 in and width is 6 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 rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l\times w\times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Substitute the known values into the formula

We know that \( V = 312\) cubic inches, \( l = 13\) inches, and \( w = 6\) inches. So, \( 312=13\times6\times h\).
First, calculate \( 13\times6 = 78\). Then the equation becomes \( 312 = 78\times h\).

Step3: Solve for \( h \)

To find \( h \), we use the formula \( h=\frac{V}{l\times w}\). So, \( h=\frac{312}{78}\).
\( h = 4\) inches.

Answer:

\( 4\) inches