Here are the step-by-step solutions for each problem on the worksheet.
Formulas used:
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Area of a circle: $A = \pi \times r^2$ (where $r$ is the radius)
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Diameter: $d = 2 \times r$ (if you have radius) or $r = d / 2$ (if you have diameter)
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Circumference: $C = \pi \times d$ (or $C = 2 \times \pi \times r$)
* We will use $\pi \approx 3.14$ for these calculations.
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Part 1: Find the Area
Problem 1
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Given: Radius ($OA$) = $22\text{ ft}$.
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Step 1: Square the radius: $22 \times 22 = 484$.
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Step 2: Multiply by $\pi$: $484 \times 3.14 = 1519.76$.
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Answer: $1,519.76\text{ sq ft}$
Problem 2
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Given: Diameter ($AB$) = $36.6\text{ in}$.
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Step 1: Find the radius: $36.6 / 2 = 18.3\text{ in}$.
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Step 2: Square the radius: $18.3 \times 18.3 = 334.89$.
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Step 3: Multiply by $\pi$: $334.89 \times 3.14 = 1051.5546$.
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Answer: $1,051.55\text{ sq in}$ (rounded)
Problem 3
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Given: Radius ($OB$) = $15.5\text{ m}$.
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Step 1: Square the radius: $15.5 \times 15.5 = 240.25$.
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Step 2: Multiply by $\pi$: $240.25 \times 3.14 = 754.385$.
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Answer: $754.39\text{ sq m}$ (rounded)
Problem 4
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Given: Radius ($XY$) = $38.2\text{ yd}$.
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Step 1: Square the radius: $38.2 \times 38.2 = 1459.24$.
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Step 2: Multiply by $\pi$: $1459.24 \times 3.14 = 4582.0136$.
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Answer: $4,582.01\text{ sq yd}$ (rounded)
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Part 2: Find Diameter and Circumference
Problem 5
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Given: Radius ($LH$) = $11.2\text{ ft}$.
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Diameter: $11.2 \times 2 = \mathbf{22.4\text{ ft}}$
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Circumference: $3.14 \times 22.4 = \mathbf{70.336\text{ ft}}$ (or $70.34\text{ ft}$)
Problem 6
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Given: Radius ($AX$) = $54.2\text{ yd}$.
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Diameter: $54.2 \times 2 = \mathbf{108.4\text{ yd}}$
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Circumference: $3.14 \times 108.4 = \mathbf{340.376\text{ yd}}$ (or $340.38\text{ yd}$)
Problem 7
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Given: Radius ($EF$) = $88.8\text{ ft}$.
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Diameter: $88.8 \times 2 = \mathbf{177.6\text{ ft}}$
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Circumference: $3.14 \times 177.6 = \mathbf{557.664\text{ ft}}$ (or $557.66\text{ ft}$)
Problem 8
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Given: Radius ($OQ$) = $0.88\text{ cm}$.
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Diameter: $0.88 \times 2 = \mathbf{1.76\text{ cm}}$
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Circumference: $3.14 \times 1.76 = \mathbf{5.5264\text{ cm}}$ (or $5.53\text{ cm}$)
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Final Answer:
1. Area = $1,519.76\text{ ft}^2$
2. Area = $1,051.55\text{ in}^2$
3. Area = $754.39\text{ m}^2$
4. Area = $4,582.01\text{ yd}^2$
5. Diameter = $22.4\text{ ft}$; Circumference = $70.34\text{ ft}$
6. Diameter = $108.4\text{ yd}$; Circumference = $340.38\text{ yd}$
7. Diameter = $177.6\text{ ft}$; Circumference = $557.66\text{ ft}$
8. Diameter = $1.76\text{ cm}$; Circumference = $5.53\text{ cm}$
Parent Tip: Review the logic above to help your child master the concept of circles geometry worksheet.
