Gabriel models the volume of a popcorn box as a right rectangular prism and the box can hold 74 cubic inches of popcorn when it is full. Its width is \( 3 \frac{1}{2} \) in and its height is 7 in . Find the length of the popcorn bo: in inches. Round your answer to the nearest tenth if necessary. Answer

To find the length of the popcorn box, we use the formula for the volume of a rectangular prism: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \] Given that the volume is 74 cubic inches, the width is \( 3.5 \) inches (which is \( 3 \frac{1}{2} \) written as an improper fraction), and the height is 7 inches, we can set up the equation: \[ 74 = \text{length} \times 3.5 \times 7 \] First, calculate \( 3.5 \times 7 \): \[ 3.5 \times 7 = 24.5 \] Now substitute back into the equation: \[ 74 = \text{length} \times 24.5 \] To find the length, divide both sides by \( 24.5 \): \[ \text{length} = \frac{74}{24.5} \] Calculating the right side: \[ \text{length} \approx 3.0 \] So, the length of the popcorn box is approximately \( 3.0 \) inches.