Question

mayas company makes solid metal balls for various industrial uses. a customer wants lead balls that have a diameter of 6 in. if maya must make 80 of these balls, how much lead will she need? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Find the radius of the ball

The diameter \(d = 6\) in. The radius \(r=\frac{d}{2}=\frac{6}{2}=3\) in.

Step2: Calculate the volume of one ball

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 3\) and \(\pi=3.14\) into the formula:

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Step3: Calculate the total volume for 80 balls

Multiply the volume of one ball by 80. \(V_{total}=113.04\times80 = 9043.2\text{ in}^3\)

Answer:

\(9043.2\)