If a Dumbwaiter has an area of 9 square feet, is 4 feet high, and its rated capacity is 13.9 lb/ft³, what is the total capacity?

To find the total capacity of the dumbwaiter, we first need to calculate its volume. The volume can be determined by multiplying the area of the base by the height. In this case, the area is given as 9 square feet, and the height is 4 feet.

Volume = Area × Height = 9 ft² × 4 ft = 36 ft³.

Next, we use the rated capacity of the dumbwaiter, which is 13.9 lb/ft³, to find the total weight capacity. Total capacity can be calculated by multiplying the volume by the rated capacity.

Total Capacity = Volume × Rated Capacity = 36 ft³ × 13.9 lb/ft³ = 500.4 lb.

Rounding this to the nearest whole number gives us approximately 500 lb. Hence, the correct answer is 500 lb, which corresponds to option C. This calculation shows how the spatial dimensions of the dumbwaiter directly influence its weight-carrying potential.