1. The problem states that the volume $V$ of a rectangular prism is given by the formula $$V = l \times w \times h$$ where $l$, $w$, and $h$ are the length, width, and height respectively. 2. We are given that $$V = 308$$ cubic millimeters, and the dimensions are $$r$$, $$7$$, and $$11$$ millimeters. 3. Substitute the known values into the volume formula: $$308 = r \times 7 \times 11$$ 4. Simplify the right side: $$308 = r \times 77$$ 5. To solve for $r$, divide both sides by 77: $$r = \frac{308}{77}$$ 6. Show the cancellation step: $$r = \frac{\cancel{308}}{\cancel{77}} = 4$$ 7. Therefore, the value of $r$ is: $$r = 4$$ millimeters. This means the missing dimension $r$ is 4 millimeters to achieve the volume of 308 cubic millimeters.