Question

latoyas company makes solid metal balls for various industrial uses. a customer wants aluminum balls that have a diameter of 6 in. if latoya must make 70 of these balls, how much aluminum will she need? use 3.14 for $pi$, and do not round your answer. $square\text{ in}^3$

Explanation:

Step1: Find the radius of the ball

The diameter $d = 6$ in, and 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 $r = 3$ in and $\pi=3.14$ into the formula: $V=\frac{4}{3}\times3.14\times3^{3}=\frac{4}{3}\times3.14\times27 = 4\times3.14\times9=113.04$ $in^{3}$.

Step3: Calculate the total volume of 70 balls

Multiply the volume of one ball by 70. So the total volume $V_{total}=70\times113.04 = 7912.8$ $in^{3}$.

Answer:

$7912.8$