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14 January, 07:09

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?

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  1. 14 January, 07:21
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    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.
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