Question

a trucking company needs to move a pile of limestone. the limestone is stored in a pile shaped like a cone. the pile is 13 yards high, and its base has a diameter of 18 yards. how many truckloads will the company need, if each truck holds 7.02 yd³ of limestone? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the radius of the cone

The diameter $d = 18$ yards, so the radius $r=\frac{d}{2}=\frac{18}{2}=9$ yards.

Step2: Calculate the volume of the cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 9$, $h = 13$ and $\pi=3.14$ into the formula. So $V=\frac{1}{3}\times3.14\times9^{2}\times13=\frac{1}{3}\times3.14\times81\times13 = 3.14\times27\times13=3.14\times351 = 1102.14$ $yd^{3}$.

Step3: Calculate the number of truck - loads

Divide the volume of the cone by the volume of each truckload. Let $n$ be the number of truck - loads. Then $n=\frac{V}{7.02}=\frac{1102.14}{7.02}=157$.

Answer:

157