Question

Otto is sitting on 10 blocks of gold. The blocks are in the shape of right trapezoidal prisms. The trapezoidal base of the prism has bases of 10 inches and 7 inches with a height of 8 inches. The lateral edge of the prism is 19 inches.

a) Upon how many total cubic inches of gold is he sitting? b) Determine the worth of Otto's gold based upon the gold pricing of $13,067.76 per troy pound. Utilize the following information:
• there are 1728 cubic inches in 1 cubic foot.
• there are 1,206.83 pounds of gold in 1 cubic foot.
• there are 0.82 pounds in 1 troy pound.

Answer 1

a) To find the volume of one block of gold, we use the formula for the volume of a right trapezoidal prism:

V = (1/2)h(b1+b2)L

where h is the height of the trapezoid, b1 and b2 are the lengths of the two parallel sides of the trapezoid, and L is the lateral edge of the prism. Substituting the given values, we get:

V = (1/2)(8)(10+7)(19) = 6844 cubic inches

Therefore, the total volume of 10 blocks of gold is:

10 x 6844 = 68440 cubic inches

b) To find the weight of the gold, we first convert the volume from cubic inches to cubic feet:

68440/1728 = 39.583 cubic feet

Next, we convert the volume to pounds:

39.583 x 1206.83 = 47800.5 pounds

Finally, we convert the weight to troy pounds:

47800.5/0.82 = 58292.07 troy pounds

The value of the gold is:

58292.07 x $13,067.76 = $760,834,385.79

Therefore, the total worth of Otto's gold based on the given information is approximately $760,834,385.79.