Question

a company makes steel rods shaped like cylinders. each rod has a diameter of 6 centimeters and a height of 20 centimeters. if the company used 45,781.2 cm³ of steel, how many rods did it make? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the radius of the rod

The diameter \(d = 6\) cm, so the radius \(r=\frac{d}{2}=\frac{6}{2}=3\) cm.

Step2: Calculate the volume of one rod

The volume formula for a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 3\) cm, \(h = 20\) cm and \(\pi=3.14\) into the formula:
\(V=3.14\times3^{2}\times20=3.14\times9\times20 = 3.14\times180=565.2\) \(cm^{3}\).

Step3: Calculate the number of rods

Let the number of rods be \(n\). We know the total volume of steel is \(45781.2\) \(cm^{3}\). Using the formula \(n=\frac{\text{Total Volume}}{\text{Volume of one rod}}\), substitute the values: \(n=\frac{45781.2}{565.2}\).
\(n = 81\).

Answer:

\(81\)