Question

a silo is in the shape of a cone. the silo is 9 meters tall, and its base has a radius of 1.5 meters. corn costs $216 per cubic meter. how much will it cost to fill the silo with corn? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of the cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 1.5\) meters and \(h=9\) meters, and \(\pi = 3.14\).
Substitute the values into the formula: \(V=\frac{1}{3}\times3.14\times(1.5)^{2}\times9\).
First, calculate \((1.5)^{2}=2.25\). Then \(\frac{1}{3}\times9 = 3\).
So \(V=3\times3.14\times2.25\).
\(3\times3.14 = 9.42\), and \(9.42\times2.25=21.195\) cubic meters.

Step2: Calculate the cost

Corn costs \(\$216\) per cubic meter.
The cost \(C=216\times V\).
Substitute \(V = 21.195\) into the formula: \(C=216\times21.195\).
\(216\times21.195=(200 + 16)\times21.195=200\times21.195+16\times21.195\).
\(200\times21.195 = 4239\), \(16\times21.195=339.12\).
\(C=4239+339.12 = 4578.12\).

Answer:

\(4578.12\)