Question

a trucking company needs to move a pile of gravel. the gravel is stored in a pile shaped like a cone. the pile is 12 yards high, and its base has a diameter of 6 yards. how many truckloads will the company need, if each truck holds 6.28 yd³ of gravel? use 3.14 for π, and do not round your answer. truckloads

Explanation:

Step1: Calculate the radius of the cone

The diameter \(d = 6\) yards. The radius \(r=\frac{d}{2}\), so \(r = \frac{6}{2}=3\) yards.

Step2: Calculate the volume of the cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(\pi = 3.14\), \(r = 3\), and \(h = 12\) into the formula.

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Step3: Calculate the number of truckloads

Each truck holds \(6.28\) \(yd^{3}\) of gravel. Let \(n\) be the number of truckloads. Then \(n=\frac{V}{6.28}\). Substitute \(V = 113.04\) into the formula.

$$n=\frac{113.04}{6.28}=18$$

Answer:

\(18\)