Question

debras company makes solid balls out of scrap metal for various industrial uses. her current task is to make a batch of iron balls with radius 6 in. if she has a total of 135,648 in³ of iron, how many balls can she make? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of one ball

The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^{3}\). Given \(r = 6\) in and \(\pi=3.14\), we substitute these values into the formula:

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Step2: Calculate the number of balls

Let \(n\) be the number of balls. We know that the total volume of iron is \(V_{total}=135648\space in^{3}\). Using the formula \(n=\frac{V_{total}}{V}\), we substitute \(V_{total} = 135648\) and \(V = 904.32\):

$$ n=\frac{135648}{904.32}=150 $$

Answer:

\(150\)