A pile of earth removed from an excavation is a cone measuring 9 ft high and 24 ft across its base. How many trips will it take to haul away the earth using a dump truck with a capacity of 9 cubic yards?

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.