Answer: It would take 6 trips
Step-by-step explanation: The pile of earth has formed into a cone with the following dimensions, height is 9 feet and base diameter is 24 feet across.
However the haulage truck has its capacity measured in yards, and so we use a standard rate of conversion of yards to feet and vice versa. The standard rate is;
1 Yard = 3 Feet
Hence, the height of the pile of earth an now be given as;
h yards = 9/3
h yards = 3
height = 3 yards
Similarly, the the base of the pile of earth can be calculated as;
(Note that the radius is derived as diameter divided by 2, that is 24/2)
r yards = 12/3
r yards = 4
radius = 4 yards
The volume of a cone is given as;
Volume = πr²h/3
Volume = 3.14 x 4² x (3/3)
Volume = 3.14 x 16
Volume = 50.24 cubic yards
For a haulage truck that can haul 9 cubic yards per trip, the total number of trips required to haul the entire volume of dirt is given as follows;
No of trips = 50.24 ÷ 9
No of trips = 5.5822
No of trips ≈ 6
Therefore it would take the truck 6 trips to haul the entire pile of earth.
, however, it is not the sine of the angle to the power of -1.