Question

lindas company makes solid spherical balls out of scrap metal for various industrial uses. a large order just came in to make lead balls with a radius of 3 in. if linda uses, on average, 28,260 in³ of lead each day making these balls, how many balls does she make, on average, each day? if necessary, refer to the list of geometry formulas. for your calculations, do not round any intermediate steps, and use the π button on the aleks calculator. round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the volume of one spherical ball

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\). Given \(r = 3\) in.
Substitute \(r = 3\) into the formula: \(V=\frac{4}{3}\pi(3)^{3}\).
First, calculate \((3)^{3}=27\). Then \(V=\frac{4}{3}\pi\times27\).
\(\frac{4}{3}\times27 = 36\), so \(V = 36\pi\) \(in^{3}\).
Using the \(\pi\) button on the calculator, \(V=36\times\pi\approx36\times3.141592654 = 113.0973355\) \(in^{3}\).

Step2: Find the number of balls

Let \(n\) be the number of balls. We know that the total volume of lead used per day is \(28260\) \(in^{3}\).
Since \(n=\frac{\text{Total volume}}{\text{Volume of one ball}}\), substitute the values: \(n=\frac{28260}{113.0973355}\).
Using the calculator, \(n\approx250.05\).

Answer:

\(250.05\)