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A trucking company needs to move a pile of dirt. The dirt is stored in a pile shaped like a cone. The pile is 12 yards high, and its base has a diameter of 8 yards. How many truckloads will the company need, if each truck holds 6.28yd3 of dirt?

Answer :

altavistard

Answer:

it will take 96 truckload trips to move the entire pile of dirt.

Step-by-step explanation:

The formula for the volume of a cone of height h and radius r is

V = πr²h.  Here, the radius, r, is half the given diameter, or r = d/2, or r = (8 yds)/2, or 4 yds, and the height is 12 yds.  Thus, in this case, the volume of the conical pile of dirt is

V = π(4 yd)²·12 yd, or

V = 3.14(16 yd²)(12 yd), or

V = 602.88 yd³

If each truck holds 6.28 yd³ and we want to know how many truckloads the company needs in order to move the conical pile, we divide the above volume (V) by 6.28 yd³:

     V                    602.88 yd³

------------- = --------------------------------------- = 96

6.28 yd³       (6.28 yd³ per truckload)

We interpret this to mean that it will take 96 truckload trips to move the entire pile of dirt.

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