The problem states that the volume of a rectangular prism is $254.80$ cubic inches. The dimensions of the prism are given as $a$, $10$ inches, and $9.1$ inches. We need to find the value of $a$.

1. Problem Description

The problem states that the volume of a rectangular prism is $254.80$ cubic inches. The dimensions of the prism are given as $a$, $10$ inches, and $9.1$ inches. We need to find the value of $a$.

2. Solution Steps

The formula for the volume $V$ of a rectangular prism is given by:

$V = l \times w \times h$

where $l$, $w$, and $h$ are the length, width, and height of the prism.

In this problem, we have $V = 254.80$ cubic inches, $l = a$, $w = 10$ inches, and $h = 9.1$ inches.

So, we can write the equation as:

$254.80 = a \times 10 \times 9.1$

$254.80 = 91a$

To find the value of $a$, we divide both sides of the equation by $91$:

$a = \frac{254.80}{91}$

$a = 2.8$

3. Final Answer

The value of $a$ is $2.8$ inches.