Question

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 6.28 yd³ of dirt? use 3.14 for π, and do not round your answer.
truckloads

Explanation:

Step1: Find the radius of the cone

The diameter \(d = 8\) yards. The radius \(r=\frac{d}{2}\), so \(r = \frac{8}{2}=4\) yards.

Step2: Calculate the volume of the cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(\pi = 3.14\), \(r = 4\) yards, and \(h = 12\) yards.

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Step3: Calculate the number of truckloads

Each truck holds \(6.28\) \(yd^{3}\). Let \(n\) be the number of truckloads. Then \(n=\frac{V}{6.28}\). Substitute \(V = 200.96\) \(yd^{3}\).

$$n=\frac{200.96}{6.28}=32$$

Answer:

\(32\)