Question 1170693: Using 1 lb. of lead, and allowing 5% for waste, determine amount of shot 1/16 in. in diameter that can be produced.
Lead weighs .410 lbs. per cu. in.
Lead shot are spheres.
Sphere volume = 4/3 * pi * r^3
1.333 * 3.1416 * .03125 * .03125 * .03125 = .0001278 cu. in.
5% waste = .95 lb. remaining.
Not sure how to proceed.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! You're on the right track! Let's break down the rest of the problem step-by-step.
**1. Calculate the Usable Lead**
* You correctly accounted for the 5% waste: 1 lb. * 0.95 = 0.95 lb. of usable lead.
**2. Calculate the Volume of Usable Lead**
* You know the weight of lead per cubic inch: 0.410 lbs/cu.in.
* Divide the usable lead by the weight per cubic inch to find the total volume:
* 0.95 lb. / 0.410 lbs/cu.in. ≈ 2.317 cu.in. of usable lead.
**3. Calculate the Volume of a Single Shot**
* You correctly calculated the volume of a single shot with a 1/16 inch diameter (radius of 1/32 inch or 0.03125 inches):
* Volume of shot ≈ 0.0001278 cu.in.
**4. Calculate the Number of Shots**
* Divide the total volume of usable lead by the volume of a single shot:
* 2.317 cu.in. / 0.0001278 cu.in./shot ≈ 18,130 shots.
**Therefore, you can produce approximately 18,130 lead shots, each 1/16 inch in diameter, from 1 lb. of lead, allowing 5% for waste.**
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