Question

a trucking company needs to move a pile of sand. the sand is stored in a pile shaped like a cone. the pile is 9 yards high, and its base has a diameter of 10 yards. how many truckloads will the company need, if each truck holds 4.71 yd³ of sand? use 3.14 for π, and do not round your answer. truckloads

Explanation:

Step1: Calculate the radius of the cone

The diameter \(d = 10\) yards, so the radius \(r=\frac{d}{2}=\frac{10}{2}=5\) yards.

Step2: Use the formula for the volume of a cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(\pi = 3.14\), \(r = 5\) yards, and \(h=9\) yards into the formula:

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Step3: Calculate the number of truckloads

If each truck holds \(4.71\space yd^{3}\) of sand, then the number of truckloads \(n=\frac{V}{4.71}\). Substitute \(V = 235.5\space yd^{3}\) into the formula:

$$n=\frac{235.5}{4.71}=50$$

Answer:

\(50\)