Question

a company makes steel rods shaped like cylinders. each rod has a diameter of 8 centimeters and a height of 30 centimeters. if the company used 94,953.6 cm³ of steel, how many rods did it make? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of one rod

The formula for the volume of a cylinder is $V = \pi r^{2}h$. Given the diameter $d = 8$ cm, so the radius $r=\frac{d}{2}=\frac{8}{2} = 4$ cm and height $h = 30$ cm. Substitute into the formula:
$$V=3.14\times4^{2}\times30$$
$$V = 3.14\times16\times30$$
$$V=1507.2\space cm^{3}$$

Step2: Calculate the number of rods

Let the number of rods be $n$. We know the total volume of steel is $94953.6\space cm^{3}$. Using the formula $n=\frac{\text{Total Volume}}{\text{Volume of one rod}}$, substitute the values:
$$n=\frac{94953.6}{1507.2}$$
$$n = 63$$

Answer:

63