Question

alans company makes solid balls out of scrap metal for various industrial uses. for one project, he must make copper balls that have a radius of 6 in. if copper costs $0.75 per in³, how much will the copper cost to make one ball? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate volume of the sphere

The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. Substitute $r=6$ and $\pi=3.14$:

$$ V = \frac{4}{3} \times 3.14 \times 6^3 $$

First compute $6^3=216$, then:

$$ V = \frac{4}{3} \times 3.14 \times 216 = 4 \times 3.14 \times 72 = 904.32 \text{ in}^3 $$

Step2: Calculate total copper cost

Multiply volume by cost per cubic inch ($\$0.75$):

$$ \text{Cost} = 904.32 \times 0.75 $$

Answer:

$\$678.24$