Final answer:
The total cost to make one copper ball with a radius of 6 inches is $678.24, calculated by first determining the volume of the sphere (904.32 cubic inches) and then multiplying by the cost per cubic inch ($0.75).
Step-by-step explanation:
To calculate the cost of the copper needed to make one spherical ball with a radius of 6 inches, we first need to find the volume of the sphere using the formula for volume: V = ¾πr³. With r being the radius (6 inches) and π approximately 3.14, we get:
V = ¾×3.14×6³ = 4×3.14×216 = 904.32 cubic inches.
The cost of copper per cubic inch is $0.75, so the total cost will be:
Cost = Volume × Cost per Cubic Inch = 904.32 × $0.75 = $678.24
The copper cost to make one ball is therefore $678.24.