Real-Life Math
You are a blacksmith who is forging some handmade bolts for a gate you recently built. The gate, which you built for a customer, requires 10 bolts. You happen to have 9 bolts that you found at an old auction and they fit the gate perfectly. However, you're 1 short, so you decide to make it so you can finish off the gate.
For the bolt to fit properly, it must be 12 inches in length and 5/8 of an inch in diameter. After reading through your old blacksmithing books and carefully studying several plans, you think you've found the best method to make bolts.
The bolt will require 2 separate pieces of iron -- 1 for the shaft, or the body of the bolt, and 1 for the head. You will make the head of the bolt by wrapping a collar around 1 end of the shaft and then forging the 2 together.
You know the bolt needs to be 12 inches long. The iron for the collar needs to be 1/4 inch thick. If the collar is less than 1/4 inch thick, the bolt may slip right through the hole. If it is larger, the bolt will look awkward and won't match the rest of the bolts you're using.
However, you still need to determine how much stock, or iron, is required to make the collar.
After reading through your book one more time, this is the equation you come up with:
- Take the diameter of the stock that is being used for the bolt's shaft.
- This number is added to the thickness of the stock that'll be used for the collar.
- Multiply this answer by 22/7 to give the correct length of stock required for the bolt's collar.
Simple enough, you think. Now you just need the information to solve the equation.
You know the bolt is 12 inches in length and that it is 5/8 of an inch in diameter. You also know the bolt requires the collar to be made out of iron that is 1/4 inch thick.
How long will the piece of stock be to make the collar?