Question

a concrete pillar has the shape of a cylinder. it has a radius of 3 meters and a height of 5 meters. if concrete costs $96 per cubic meter, how much did the concrete cost for the pillar? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 3\) meters, \(h=5\) meters, and \(\pi = 3.14\).
Substitute the values into the formula: \(V=3.14\times3^{2}\times5\).
First, calculate \(3^{2}=9\). Then \(V = 3.14\times9\times5\).
\(3.14\times9=28.26\), and \(28.26\times5 = 141.3\) cubic meters.

Step2: Calculate the cost

Since the cost per cubic meter is \(\$96\), and the volume \(V = 141.3\) cubic meters.
The total cost \(C=96\times V\).
Substitute \(V = 141.3\) into the formula: \(C=96\times141.3\).
\(96\times141.3=(100 - 4)\times141.3=100\times141.3-4\times141.3\).
\(100\times141.3 = 14130\), \(4\times141.3 = 565.2\).
\(14130-565.2=13564.8\)

Answer:

\(13564.8\)