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Circle Formulas

Grade 7 · Geometry · Worksheet 1

  1. Olivia is designing a circular garden pond for her backyard. The pond will have a radius of 3 meters. She wants to install a decorative rope light around the entire outer edge of the pond and cover the bottom surface with a special waterproof liner. How many meters of rope light does Olivia need for the circumference, and how many square meters of liner does she need for the area? Use π ≈ 3.14.
    Answer: ______________
  2. A circular garden has a stone path around its outer edge. The garden's diameter is 14 meters. If the stone path extends 2 meters beyond the garden's edge all the way around, what is the circumference of the outer edge of the path? (Use π = 3.14)
    Answer: ______________
  3. Matiu is helping his school design a new circular sensory garden. The garden will have a diameter of 22 meters. A decorative path made of paving stones will go around the entire outer edge, and the whole circular area will be filled with special soft mulch. How many meters of paving stones are needed for the path (circumference), and how many square meters of mulch are needed to cover the garden? Use π ≈ 3.14.
    Answer: ______________
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Answer Key & Explanations

Circle Formulas · Grade 7 · Worksheet 1

  1. Olivia is designing a circular garden pond for her backyard. The pond will have a radius of 3 meters. She wants to install a decorative rope light around the entire outer edge of the pond and cover the bottom surface with a special waterproof liner. How many meters of rope light does Olivia need for the circumference, and how many square meters of liner does she need for the area? Use π ≈ 3.14. Answer: 18.84 meters, 28.26 square meters Solution: The radius of the pond is 3 meters. Calculate the circumference (rope light) using C = 2πr. C = 2 × 3.14 × 3 = 6.28 × 3 = 18.84 meters.
    Full step-by-step solution

    Step 1: The radius of the pond is 3 meters. Step 2: Calculate the circumference (rope light) using C = 2πr. C = 2 × 3.14 × 3 = 6.28 × 3 = 18.84 meters. Step 3: Calculate the area (liner) using A = πr². A = 3.14 × (3 × 3) = 3.14 × 9 = 28.26 square meters. Step 4: Final answer: Olivia needs 18.84 meters of rope light and 28.26 square meters of liner.

  2. A circular garden has a stone path around its outer edge. The garden's diameter is 14 meters. If the stone path extends 2 meters beyond the garden's edge all the way around, what is the circumference of the outer edge of the path? (Use π = 3.14) Answer: 56.52 meters Solution: The garden is circular with diameter 14 m. The stone path extends 2 m beyond the garden's edge all around. We want the circumference of the outer edge of the path.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Understand the problem** The garden is circular with diameter 14 m. The stone path extends 2 m beyond the garden's edge all around. We want the circumference of the outer edge of the path. --- **Step 2: Find the radius of the outer edge of the path** Garden radius = diameter / 2 = 14 / 2 = 7 m. The path extends 2 m beyond the garden's edge, so the outer edge radius is: Outer radius = garden radius + 2 = 7 + 2 = 9 m. --- **Step 3: Recall the circumference formula** Circumference = 2 * π * radius. --- **Step 4: Plug in the numbers** Circumference = 2 * 3.14 * 9. First, 2 * 9 = 18. Then, 18 * 3.14 = 56.52. --- **Step 5: State the final answer** The circumference of the outer edge of the path is 56.52 meters.

  3. Matiu is helping his school design a new circular sensory garden. The garden will have a diameter of 22 meters. A decorative path made of paving stones will go around the entire outer edge, and the whole circular area will be filled with special soft mulch. How many meters of paving stones are needed for the path (circumference), and how many square meters of mulch are needed to cover the garden? Use π ≈ 3.14. Answer: 69.08 meters, 379.94 square meters Solution: Find the radius. Radius = diameter ÷ 2 = 22 ÷ 2 = 11 meters. Calculate the circumference (path length).
    Full step-by-step solution

    Step 1: Find the radius. Radius = diameter ÷ 2 = 22 ÷ 2 = 11 meters. Step 2: Calculate the circumference (path length). C = π × diameter = 3.14 × 22 = 69.08 meters. Step 3: Calculate the area (mulch needed). A = π × radius² = 3.14 × (11 × 11) = 3.14 × 121 = 379.94 square meters. The paving stones needed are 69.08 meters, and the mulch needed is 379.94 square meters.