Circle Logic Packet
Carnival Circles
Midway Mathematics
Guest Name
Entry Date
AREA FORMULA
r
Area Formula
A = πr²
1. Find Radius (r)
2. Square it (r × r)
3. Multiply by π (3.14)
Walkthrough: The Giant Lollipop
r = 10 cm
Radius (r) = 10
Step 2 A = π × 10²
Step 3 A = π × 100
Total Area ≈ 314.16
Warm-Up: Midway Trials
1. Cotton Candy Base (r = 8 in)
2. Target Practice (r = 12 cm)
Midway Calculations
Round final results to the nearest hundredth.
Use the π button. Divide Diameter by 2 first!
MIDWAY RADII
r=3.5
3. Ring Toss Hoop
r=4.2
4. Soda Cup Lid
DIAMETER DANGER
d=14cm
5. Popcorn Bucket Base
d=24.2
6. Game Quarter (Diameter)
Grand Prize Problems
Real World Rounds
7. Giant Funnel Cake (d = 36 in)
Area: ________________ inches²
8. Grand Carousel (r = 18 ft)
Area: ________________ feet²
9. Ferris Wheel (r = 42 m)
Area: ________________ meters²
THE JACKPOT BONUS
Stage Area = 201.06 sq ft. Find the Radius (r).
Radius: ________________ ft
Circle Logic Answer Key
Winner's Guide
Answer Key: Carnival Circles
TEACHER ADMISSION
P1 Midway Trials
1. Cotton Candy (r=8)
A = π × 8² = 64π
201.06 in²
2. Target (r=12)
A = π × 12² = 144π
452.39 cm²
P2 Midway Calculations
3. Ring Toss (r=3.5)
12.25π
38.48 in²
4. Soda Lid (r=4.2)
17.64π
55.42 cm²
5. Popcorn (d=14 → r=7)
49π
153.94 cm²
6. Quarter (d=24.2 → r=12.1)
146.41π
459.96 mm²
P3 Grand Prize Key
7. Funnel Cake (r=18)
Standardized to 2 decimal places
A = 18² × π = 324π
1,017.88 in²
8. Carousel (r=18)
A = 18² × π = 324π
1,017.88 ft²
9. Ferris Wheel (r=42)
A = 42² × π = 1764π
5,541.77 m²
JACKPOT BONUS SOLUTION
201.06 = π × r²
64.00 ≈ r²
√64 = r
Final Radius
r = 8 ft