The Eternal’s Workbook

Edition 15, Lesson 15.2: Circumference and Pi

Part I: Walking the Boundary

Use the formula $C = 2\pi r$ or $C = \pi d$. Use 3.14 for $\pi$.

1. A circular table has a **Diameter** of 10 feet. What is its Circumference?
C = ________ feet
2. A gold ring has a **Radius** of 8 mm. What is the distance around the ring?
C = ________ mm
3. The "Molten Sea" has a diameter of 30 cubits (in our new measure). What is its precise circumference?
C = ________ cubits
The Lawyer's Check:

Did you check if you were given the Radius or the Diameter? If you have the radius, you must double it before multiplying by Pi!

Part II: The Inverse Walk (Finding the Root)

If you know the Circumference, can you find the Diameter? $d = C / \pi$.

4. A tree trunk has a circumference of 15.7 feet. What is its diameter?
d = ________ feet
5. A circular track is 400 meters long (Circumference). What is the radius of the field inside?
r = ________ meters
6. A round tower has a circumference of 62.8 cubits. How wide is the tower?
d = ________ cubits

Part III: The Precision Challenge (Comparing Pi)

Calculate the Circumference of a circle with $d=10$ using three different values for $\pi$.

7. The Biblical Estimate: $\pi \approx 3$.
C = ________
The Student's Estimate: $\pi \approx 3.14$.
C = ________
The Engineer's Estimate: $\pi \approx 3.14159$.
C = ________
Reflection: How much difference does the extra precision make?

Part IV: Kingdom Modeling

8. The Orbit of Grace:
A satellite orbits the earth at a height of 200 miles. The radius of the Earth is 4,000 miles.
1. Find the total radius of the orbit ($r = 4000 + 200$).
2. Calculate the distance of one full orbit.
Orbit Distance: ________ miles
9. The Wheel of the Gospel:
A chariot wheel has a diameter of 2 cubits. How many times must it turn to travel 100 cubits?
(Hint: Find the circumference first. Then divide the total distance by the circumference.)
Turns: ________
10. The Boundary of the Camp:
The camp of Israel is arranged in a circle around the Tabernacle. If the camp must have a perimeter of exactly 12,000 cubits to fit all the tribes, what must the radius be?
Radius: ________ cubits

Part V: The Echad Extension (Transmission)

11. The Pi Hunt:
With a younger sibling or friend, find three circular objects in your house. Measure their distance around (string) and distance across (ruler). Divide C/d for each one. Did you get close to 3.14? Show them the magic of the number.

Part VI: Logic and Reflection

12. The Mystery of the Decimal:
Why do we use 3.14 instead of the full number for Pi? What does this teach us about the difference between "Divine Precision" and "Human Approximation"?
13. The Solomon Defense:
If a skeptic says, "The Bible is wrong because it says Pi is 3," how would you answer them using the logic of "Workman's Measure"?
14. The Infinite Remainder:
If $\pi$ is an irrational number that never ends, does that mean we can never truly finish measuring a circle? What does this teach us about the difference between "Finishing a task" and "Knowing a truth"?

Part VII: The Science of Estimation (Mental Math)

Without a calculator, estimate the circumference using $\pi \approx 3$. Then calculate the error.

15. The Quick Check:
Diameter = 50 cm.
Estimated C ($3 \times 50$): ________
Actual C ($3.14 \times 50$): ________
Difference: ________
Why is estimation a useful skill for a Builder?
16. The Carpenter's Rule:
A carpenter needs to wrap a metal band around a circular table with a radius of 7 feet. He has 45 feet of metal.
Estimate first: Is 45 feet enough? ($2 \times 3 \times 7 = ?$)
Calculate: $2 \times 3.14 \times 7 = ?$
Does he have enough metal? ________
"I vow to respect the infinite within the finite. I will honor the Mystery of Pi, knowing that the Father's truth goes on forever. I will use my tools with care, but I will trust in the God who is greater than my measure. I will walk the perimeter of grace with patience and wonder."
[VOLUME 2 WORKBOOK SPEC: 15.2] This workbook focuses on the calculation of circumference and the manipulation of the $\pi$ formula. It introduces the concept of inverse calculation (finding d from C). Total Practice Items: 9 Theological Anchor: Infinity/Approximation