Here are the step-by-step solutions for each problem on the worksheet.
Important Formulas:
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Circumference ($C$): $2 \times 3.14 \times \text{radius}$ (or $3.14 \times \text{diameter}$)
*
Area ($A$): $3.14 \times \text{radius} \times \text{radius}$
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Problem 1
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Given: Radius ($r$) = $40\text{ ft}$
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Step 1 (Circumference): $2 \times 3.14 \times 40 = 6.28 \times 40 = 251.2$
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Step 2 (Area): $3.14 \times 40 \times 40 = 3.14 \times 1600 = 5024$
Problem 2
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Given: Diameter ($d$) = $56\text{ cm}$
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Find Radius first: $56 \div 2 = 28\text{ cm}$
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Step 1 (Circumference): $3.14 \times 56 = 175.84$
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Step 2 (Area): $3.14 \times 28 \times 28 = 3.14 \times 784 = 2461.76$
Problem 3
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Given: Radius ($r$) = $62\text{ in}$
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Step 1 (Circumference): $2 \times 3.14 \times 62 = 6.28 \times 62 = 389.36$
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Step 2 (Area): $3.14 \times 62 \times 62 = 3.14 \times 3844 = 12070.16$
Problem 4
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Given: Radius ($r$) = $12\text{ cm}$
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Step 1 (Circumference): $2 \times 3.14 \times 12 = 6.28 \times 12 = 75.36$
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Step 2 (Area): $3.14 \times 12 \times 12 = 3.14 \times 144 = 452.16$
Problem 5
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Given: Diameter ($d$) = $102\text{ mm}$
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Find Radius first: $102 \div 2 = 51\text{ mm}$
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Step 1 (Circumference): $3.14 \times 102 = 320.28$
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Step 2 (Area): $3.14 \times 51 \times 51 = 3.14 \times 2601 = 8167.14$
Problem 6
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Given: Radius ($r$) = $15.5\text{ ft}$
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Step 1 (Circumference): $2 \times 3.14 \times 15.5 = 6.28 \times 15.5 = 97.34$
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Step 2 (Area): $3.14 \times 15.5 \times 15.5 = 3.14 \times 240.25 = 754.385$
Problem 7
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Given: Diameter ($d$) = $30.5\text{ m}$
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Find Radius first: $30.5 \div 2 = 15.25\text{ m}$
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Step 1 (Circumference): $3.14 \times 30.5 = 95.77$
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Step 2 (Area): $3.14 \times 15.25 \times 15.25 = 3.14 \times 232.5625 = 730.24625$
Problem 8
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Given: Radius ($r$) = $3.5\text{ km}$
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Step 1 (Circumference): $2 \times 3.14 \times 3.5 = 6.28 \times 3.5 = 21.98$
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Step 2 (Area): $3.14 \times 3.5 \times 3.5 = 3.14 \times 12.25 = 38.465$
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Final Answer:
1)
C = 251.2 ft
A = 5,024 sq ft
2)
C = 175.84 cm
A = 2,461.76 sq cm
3)
C = 389.36 in
A = 12,070.16 sq in
4)
C = 75.36 cm
A = 452.16 sq cm
5)
C = 320.28 mm
A = 8,167.14 sq mm
6)
C = 97.34 ft
A = 754.385 sq ft
7)
C = 95.77 m
A = 730.24625 sq m
8)
C = 21.98 km
A = 38.465 sq km
Parent Tip: Review the logic above to help your child master the concept of area and circumference of circles worksheet.
