Question

The North County Sand and Gravel Company stockpiles sand to use on the icy roads in the northern rural counties of the state. Sand is brought in by tandem trailers that carry 12 m3 each. The engineers know that when the pile of sand, which is in the shape of a cone, is 17 m across and 9 m high they will have enough for a normal winter. How many truckloads are needed to build the pile?

Answer 1

The North County Sand and Gravel Company needs 54 truckloads to build a sand pile 17 meters in diameter and 9 meters tall, with each truck carrying 12 cubic meters of sand.

Step-by-step explanation:

The student has asked how many truckloads are needed to build a sand pile in the shape of a cone with a diameter of 17 meters and a height of 9 meters. Each tandem trailer carries 12 cubic meters (m3) of sand. To calculate the number of truckloads required, we first need to find the volume of the sand cone. The formula for the volume of a cone is V = \(\frac{1}{3}\)\pi r2h, where V is the volume, r is the radius, and h is the height. In this case, since the diameter is 17 meters, the radius (r) is half of that, 8.5 meters. Therefore, the volume (V) is:

V = \(\frac{1}{3}\)\pi (8.5 m)2(9 m) \approx 643.5 m3.

Now, we divide the total volume by the volume that each truck can carry:

Number of loads = \(\frac{Total Volume}{Volume per Truck}\) = \(\frac{643.5 m3}{12 m3}\)

Number of loads = 53.625

Since you cannot have a fraction of a truckload, you would need to round up to the next whole number. Therefore, North County Sand and Gravel Company will need 54 truckloads to build the pile.