Final answer:
Using the volume formula for a sphere, Trey's company can make approximately 200 balls from 76,302 cubic inches of metal, but none of the provided multiple-choice options match this calculation.
Step-by-step explanation:
The question asks how many solid balls Trey's company can make from 76,302 cubic inches of metal, each with a radius of 4.5 inches. To find the volume of one solid ball, we use the formula for the volume of a sphere, × (4/3)πr³, where π is approximately 3.14159, and the radius r is 4.5 inches. We then divide the total available volume of metal by the volume of one ball to determine how many balls can be made.
Finding the volume of a single ball:
Volume of a sphere = (4/3)πr³
= (4/3) × 3.14159 × (4.5 inches)³
= (4/3) × 3.14159 × 91.125 cubic inches
= 381.703 cubic inches (approximately).
We then calculate how many balls can be made:
76,302 cubic inches ÷ 381.703 cubic inches/ball = 200 balls (approximately).
Since none of the provided answer options (a) 33,890 balls, (b) 5,700 balls, (c) 17,000 balls, or (d) 10,000 balls match our calculation, it appears there may be a typo or mistake in the options given. Based on the available information and our calculations, Trey's company can make approximately 200 solid metal balls.