Questions: Question 29 (2 points) A restaurant owner has a large trash container in the shape of a rectangular prism with a height of 4 ft and base that is 3 ft wide by 2 ft long. During a two-month period the container needed to be emptied 9 times. How many cubic feet of trash were taken away during the two months? Enter just the number with no units cubed. A

Solution Steps

The container is a rectangular prism with a height of 4 ft, a width of 3 ft, and a length of 2 ft. The volume \( V \) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] Substitute the given values: \[ V = 2 \, \text{ft} \times 3 \, \text{ft} \times 4 \, \text{ft} \] \[ V = 24 \, \text{cubic feet} \]

The container was emptied 9 times during the two-month period. To find the total volume of trash removed, multiply the volume of the container by the number of times it was emptied: \[ \text{Total volume} = V \times \text{number of times emptied} \] \[ \text{Total volume} = 24 \, \text{cubic feet} \times 9 \] \[ \text{Total volume} = 216 \, \text{cubic feet} \]

The total volume of trash taken away during the two months is: \[ 216 \]

Final Answer