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Circle Formulas

Grade 7 · Geometry · Worksheet 3

  1. Mason is building a circular outdoor fire pit in his backyard. The fire pit will have a diameter of 12 feet. He needs to install a steel ring around the entire outer edge to hold the stones in place, and he wants to fill the entire circular base with a layer of fireproof sand. What is the length of the steel ring needed for the circumference, and what is the area of the base that needs to be covered with sand? Use π ≈ 3.14.
    Answer: ______________
  2. Liam is designing a circular garden with a diameter of 14 meters for his community park. He needs to install decorative fencing around the entire perimeter and calculate the area to determine how much soil to order for planting flowers. What is the circumference of Liam's garden in meters, and what is its area in square meters?
    Answer: ______________
  3. A circular pizza has a diameter of 30 cm. Isabella cuts it into 8 equal slices. What is the area of one slice? (Use π = 3.14)
    Answer: ______________
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Answer Key & Explanations

Circle Formulas · Grade 7 · Worksheet 3

  1. Mason is building a circular outdoor fire pit in his backyard. The fire pit will have a diameter of 12 feet. He needs to install a steel ring around the entire outer edge to hold the stones in place, and he wants to fill the entire circular base with a layer of fireproof sand. What is the length of the steel ring needed for the circumference, and what is the area of the base that needs to be covered with sand? Use π ≈ 3.14. Answer: 37.68 feet, 113.04 square feet Solution: Identify the diameter of the fire pit: 12 feet. Calculate the radius: radius = diameter ÷ 2 = 12 ÷ 2 = 6 feet. Calculate the circumference (length of steel ring): C = π × diameter = 3.14 × 12 = 37.68 feet.
    Full step-by-step solution

    Step 1: Identify the diameter of the fire pit: 12 feet. Step 2: Calculate the radius: radius = diameter ÷ 2 = 12 ÷ 2 = 6 feet. Step 3: Calculate the circumference (length of steel ring): C = π × diameter = 3.14 × 12 = 37.68 feet. Step 4: Calculate the area (sand coverage): A = π × radius² = 3.14 × (6 × 6) = 3.14 × 36 = 113.04 square feet. The steel ring needed is 37.68 feet and the area for sand is 113.04 square feet.

  2. Liam is designing a circular garden with a diameter of 14 meters for his community park. He needs to install decorative fencing around the entire perimeter and calculate the area to determine how much soil to order for planting flowers. What is the circumference of Liam's garden in meters, and what is its area in square meters? Answer: Circumference: 44 meters, Area: 154 square meters Solution: Diameter of the circular garden = 14 meters. Radius = Diameter / 2 Radius = 14 / 2 = 7 meters. Circumference formula for a circle: C = 2 * π * radius We use π ≈ 22/7 for easier calculation.
    Full step-by-step solution

    Let's solve this step by step. --- **Step 1: Identify the given information** Diameter of the circular garden = 14 meters. --- **Step 2: Find the radius** Radius = Diameter / 2 Radius = 14 / 2 = 7 meters. --- **Step 3: Calculate the circumference** Circumference formula for a circle: C = 2 * π * radius We use π ≈ 22/7 for easier calculation. C = 2 * (22/7) * 7 C = 2 * 22 C = 44 meters. So, the circumference is **44 meters**. --- **Step 4: Calculate the area** Area formula for a circle: A = π * radius^2 A = (22/7) * (7^2) A = (22/7) * 49 A = 22 * 7 A = 154 square meters. So, the area is **154 square meters**. --- **Final Answer:** Circumference: 44 meters Area: 154 square meters

  3. A circular pizza has a diameter of 30 cm. Isabella cuts it into 8 equal slices. What is the area of one slice? (Use π = 3.14) Answer: 88.3125 cm² Solution: Find the radius. Radius = diameter ÷ 2 = 30 ÷ 2 = 15 cm. Calculate the total area of the pizza.
    Full step-by-step solution

    Step 1: Find the radius. Radius = diameter ÷ 2 = 30 ÷ 2 = 15 cm. Step 2: Calculate the total area of the pizza. Area = π × r² = 3.14 × 15² = 3.14 × 225 = 706.5 cm². Step 3: Divide the total area by the number of slices. Area of one slice = 706.5 ÷ 8 = 88.3125 cm². The answer is 88.3125 cm².