Final answer:
Otto is sitting on 680 cubic inches of gold. The worth of Otto's gold is $34,464.65.
Step-by-step explanation:
To find the total cubic inches of gold Otto is sitting on, we first need to find the volume of one block of gold. The trapezoidal base of the prism has bases of 10 inches and 7 inches with a height of 8 inches. The formula to find the volume of a trapezoidal prism is V = ((a + b) / 2) * h, where a and b are the bases and h is the height. Plugging in the values, we get V = ((10 + 7) / 2) * 8 = 68 cubic inches for one block. Since Otto is sitting on 10 blocks, the total volume of gold is 68 * 10 = 680 cubic inches.
To determine the worth of Otto's gold, we need to convert cubic inches to troy pounds. First, we convert cubic inches to cubic feet by dividing by 1728 (since there are 1728 cubic inches in 1 cubic foot). Then, we convert cubic feet to pounds by multiplying by the density of gold, which is 1206.83 pounds per cubic foot. Next, we divide by the conversion factor of 0.82 pounds in 1 troy pound. Finally, we multiply by the price of gold per troy pound to determine the worth. Plugging in the values, we get worth = (680 / 1728) * 1206.83 / 0.82 * 13067.76 = $34,464.65.