Circle Formulas

lessonbunny.com

Answer Key & Explanations

Circle Formulas · Grade 7 · Worksheet 2

1. A city is building a circular skate park with a diameter of 28 meters. The planners need to install a protective railing around the entire outer edge and calculate how much special rubber surfacing material is needed to cover the entire circular area. What is the total length of railing required (circumference) and how many square meters of surfacing material are needed (area)? Use π ≈ 3.14 and round your answers to the nearest whole number. Answer: 88 meters, 616 square meters Solution: Find the radius of the skate park. The diameter is 28 meters, so the radius is half of that: 28 ÷ 2 = 14 meters. Calculate the circumference (length of railing needed).
   Full step-by-step solution

   Step 1: Find the radius of the skate park. The diameter is 28 meters, so the radius is half of that: 28 ÷ 2 = 14 meters. Step 2: Calculate the circumference (length of railing needed). The formula is C = π × diameter. Using π ≈ 3.14: C = 3.14 × 28 = 87.92 meters. Rounded to the nearest whole number: 88 meters. Step 3: Calculate the area (amount of surfacing material needed). The formula is A = π × radius². Using π ≈ 3.14 and radius = 14 meters: A = 3.14 × (14 × 14) = 3.14 × 196 = 615.44 square meters. Rounded to the nearest whole number: 616 square meters. Step 4: Combine the answers. The city needs 88 meters of railing and 616 square meters of surfacing material.

2. A circular fountain has a radius of 6 meters. What is its circumference? Use C = 2πr. Answer: 12π meters Solution: Write down the formula for circumference: C = 2πr. Substitute the given radius r = 6 into the formula: C = 2π(6). Multiply 2 and 6: 2 × 6 = 12.
   Full step-by-step solution

   Step 1: Write down the formula for circumference: C = 2πr. Step 2: Substitute the given radius r = 6 into the formula: C = 2π(6). Step 3: Multiply 2 and 6: 2 × 6 = 12. Step 4: The circumference is 12π meters. The answer is 12π meters.

3. Liam is designing a circular fountain for his community garden. The fountain will have a diameter of 14 feet. He needs to purchase decorative tiles to cover the entire area of the fountain and a special border to go around its circumference. How many square feet of tiles does Liam need to cover the fountain's area, and how many feet of border does he need for the circumference? Use π ≈ 3.14 for your calculations. Answer: 153.86 square feet of tiles and 43.96 feet of border Solution: - Diameter = 14 feet 1. Area for tiles (square feet) 2.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** We have a circular fountain with: - Diameter = 14 feet - Need: 1. Area for tiles (square feet) 2. Circumference for border (feet) - Use π ≈ 3.14 --- **Step 2: Find the radius** Radius = Diameter / 2 Radius = 14 / 2 = 7 feet --- **Step 3: Calculate the area of the fountain** Area of a circle = π × (radius)^2 Area = 3.14 × (7)^2 First, 7^2 = 49 Area = 3.14 × 49 Now multiply: 3.14 × 49 = 3.14 × (50 - 1) = 3.14 × 50 - 3.14 × 1 = 157.00 - 3.14 = 153.86 So, area = 153.86 square feet. This is the amount of tiles needed. --- **Step 4: Calculate the circumference** Circumference of a circle = π × diameter Circumference = 3.14 × 14 Multiply: 3.14 × 14 = 3.14 × (10 + 4) = 31.40 + 12.56 = 43.96 So, circumference = 43.96 feet. This is the length of the border needed. --- **Step 5: Final answer** Tiles needed: 153.86 square feet Border needed: 43.96 feet