Here are the step-by-step solutions for the problems shown in the worksheet.
1. Fencing for the Playground
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Goal: Find the length of the fence needed to go around the circle (the circumference).
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Given: The diameter ($d$) is 64 meters. Use $\pi = 3.14$.
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Formula: Circumference $C = \pi \times d$
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Calculation:
$$C = 3.14 \times 64$$
$$C = 200.96 \text{ m}$$
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Rounding: This is approximately 201 m.
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Match: Option C.
2. Ferris Wheel Rotation
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Goal: Find the distance traveled in one complete turn (the circumference).
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Given: The diameter ($d$) is 250 feet. Use $\pi = 3.14$.
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Formula: Circumference $C = \pi \times d$
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Calculation:
$$C = 3.14 \times 250$$
$$C = 785 \text{ ft}$$
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Match: Option D.
3. Radius from Circumference (Meters)
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Goal: Find the radius ($r$).
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Given: The circumference ($C$) is 36.31 meters. Use $\pi = 3.14$.
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Formula: $C = 2 \times \pi \times r$, so $r = C / (2 \times \pi)$
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Step 1: Find the diameter first ($d = C / \pi$).
$$d = 36.31 / 3.14 = 11.56 \text{ m}$$
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Step 2: Divide the diameter by 2 to get the radius.
$$r = 11.56 / 2 = 5.78 \text{ m}$$
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Rounding: The closest whole number option is 6 m.
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Match: Option D.
4. Radius from Circumference (Feet)
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Goal: Find the radius ($r$).
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Given: The circumference ($C$) is 18.41 feet. Use $\pi = 3.14$.
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Formula: $r = C / (2 \times \pi)$
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Step 1: Find the diameter first ($d = C / \pi$).
$$d = 18.41 / 3.14 = 5.86 \text{ ft}$$
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Step 2: Divide the diameter by 2 to get the radius.
$$r = 5.86 / 2 = 2.93 \text{ ft}$$
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Rounding: This is very close to 3 ft.
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Match: Option C.
5. Bicycle Trail Distance
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Goal: Find the total distance biked after 4 laps.
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Given: Diameter ($d$) is 3 miles. Laps = 4. Use $\pi = 3.14$.
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Step 1: Find the distance of one lap (Circumference).
$$C = 3.14 \times 3 = 9.42 \text{ miles}$$
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Step 2: Multiply by the number of laps.
$$\text{Total Distance} = 9.42 \times 4$$
$$\text{Total Distance} = 37.68 \text{ miles}$$
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Rounding: The question asks "About how far," so we look for the closest option. 37.68 is closer to 40 than it is to 33.
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Match: Option A.
Final Answer:
1. C
2. D
3. D
4. C
5. A
Parent Tip: Review the logic above to help your child master the concept of 8th grade math word problems worksheet.
