Question

a company makes steel rods shaped like cylinders. each rod has a diameter of 4 centimeters and a height of 60 centimeters. if the company used 54,259.2 cm³ of steel, how many rods did it make? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Find radius of cylinder

Diameter \( d = 4 \) cm, so radius \( r=\frac{d}{2}=\frac{4}{2} = 2 \) cm.

Step2: Calculate volume of one cylinder

Volume of cylinder formula: \( V=\pi r^{2}h \). Substitute \( \pi = 3.14 \), \( r = 2 \) cm, \( h = 60 \) cm.
\( V=3.14\times2^{2}\times60=3.14\times4\times60 = 753.6 \) \( \text{cm}^3 \).

Step3: Find number of rods

Total volume of steel is \( 54259.2 \) \( \text{cm}^3 \). Number of rods \( n=\frac{\text{Total Volume}}{\text{Volume of one rod}}=\frac{54259.2}{753.6}=72 \).

Answer:

72