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Circle Formulas

Grade 7 · Geometry · Worksheet 3

  1. A circular clock has a radius of 14 cm. What is its circumference? (Use π = 3.14)
    Answer: ______________
  2. A circular pond has a radius of 14 meters. Hana wants to build a fence around it and cover the surface with tiles. What is the circumference and area of the pond?
    Answer: ______________
  3. A circular fountain in a park has a radius of 7 meters. Isabella wants to know the circumference and area of the fountain. Find both values using π = 3.14.
    Answer: ______________
  4. π × (14² - 7²) = ? Answer: ______________
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Answer Key & Explanations

Circle Formulas · Grade 7 · Worksheet 3

  1. A circular clock has a radius of 14 cm. What is its circumference? (Use π = 3.14) Answer: 87.92 cm Solution: The formula for circumference is C = 2πr. Substitute the given values: r = 14 cm and π = 3.14. C = 2 × 3.14 × 14.
    Full step-by-step solution

    Step 1: The formula for circumference is C = 2πr. Step 2: Substitute the given values: r = 14 cm and π = 3.14. Step 3: C = 2 × 3.14 × 14. Step 4: First multiply 2 × 14 = 28. Step 5: Then multiply 28 × 3.14 = 87.92. Step 6: The circumference is 87.92 cm. The answer is 87.92 cm.

  2. A circular pond has a radius of 14 meters. Hana wants to build a fence around it and cover the surface with tiles. What is the circumference and area of the pond? Answer: Circumference = 88 m, Area = 616 m² Solution: Use the formula for circumference: C = 2πr. Substitute r = 14 and π = 22/7. C = 2 × (22/7) × 14 = 2 × 22 × 2 = 88 m.
    Full step-by-step solution

    Step 1: Use the formula for circumference: C = 2πr. Substitute r = 14 and π = 22/7. C = 2 × (22/7) × 14 = 2 × 22 × 2 = 88 m. Step 2: Use the formula for area: A = πr². Substitute r = 14 and π = 22/7. A = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 m². Step 3: The circumference is 88 m and the area is 616 m².

  3. A circular fountain in a park has a radius of 7 meters. Isabella wants to know the circumference and area of the fountain. Find both values using π = 3.14. Answer: Circumference = 43.96 m, Area = 153.86 m² Solution: Use the formula for circumference: C = 2πr. Substitute r = 7 and π = 3.14: C = 2 × 3.14 × 7. Step 2: Multiply 2 × 3.14 = 6.28.
    Full step-by-step solution

    Step 1: Use the formula for circumference: C = 2πr. Substitute r = 7 and π = 3.14: C = 2 × 3.14 × 7. Step 2: Multiply 2 × 3.14 = 6.28. Then multiply 6.28 × 7 = 43.96. So circumference = 43.96 m. Step 3: Use the formula for area: A = πr². Substitute r = 7: r² = 7 × 7 = 49. Then A = 3.14 × 49. Step 4: Multiply 3.14 × 49 = 153.86. So area = 153.86 m². The final answers are circumference = 43.96 m and area = 153.86 m².

  4. π × (14² - 7²) = ? Answer: 147π Solution: We have: π × (14² - 7²) Calculate the squares inside the parentheses. 14² = 14 × 14 = 196 7² = 7 × 7 = 49 Subtract the squares. 196 - 49 = 147 Multiply by π.
    Full step-by-step solution

    Let's solve step by step. We have: π × (14² - 7²) Step 1: Calculate the squares inside the parentheses. 14² = 14 × 14 = 196 7² = 7 × 7 = 49 Step 2: Subtract the squares. 196 - 49 = 147 Step 3: Multiply by π. π × 147 = 147π So the final answer is 147π. Explanation: We used the order of operations (parentheses first, then multiplication) and computed the squares before subtracting. The π remains as a symbol in the final answer.