Area and Circumference of Circle- WS1

Circle Problems: Area & Circumference Practice - The Study Zone

Circle Problems: Area & Circumference Practice (Part 1)

1) The Grade 7 class is having a pizza party! Mr. Jones ordered a giant circular pizza with a diameter of 60 cm.

  1. What is the circumference of this delicious pizza? Show your work.
    Formula: $C = \pi d$
    Substitute: $C = 3.14 \times 60 \text{ cm}$
    Calculate: $C = 188.4 \text{ cm}$
    Answer: 188.4 cm
  2. If each student needs at least 75 cm² of pizza, how many students can this one giant pizza feed? Show your work.
    Radius: $r = 60/2 = 30 \text{ cm}$
    Area: $3.14 \times 30^2 = 2826 \text{ cm}²$
    Students: $2826 ÷ 75 ≈ 37.68$
    Answer: 37 students

2) The school's circular garden has a radius of 3.5 meters. To keep the plants watered, the caretaker installs a sprinkler in the center of the garden.

  1. What is the area of the garden that the sprinkler needs to cover? Show your work.
    Formula: $A = \pi r^2$
    Calculate: $3.14 \times 3.5^2 = 38.465 \text{ m}²$
    Answer: 38.465 m²
  2. If the water from the sprinkler reaches a distance of 4 meters in all directions, will it cover the entire garden? Explain your reasoning.
    Sprinkler Radius: 4 m
    Garden Radius: 3.5 m
    Comparison: 4 m > 3.5 m
    Answer: Yes, full coverage

3) A local park has a circular running track with a circumference of 400 meters.

  1. What is the diameter of this running track? Show your work.
    Formula: $d = C/\pi$
    Calculate: $400/3.14 ≈ 127.39 \text{ m}$
    Answer: 127.39 m
  2. Sarah runs 5 laps around the track. How far does she run in total?
    Calculate: $400 \times 5 = 2000 \text{ m}$
    Answer: 2000 meters
  3. If the park wants to plant grass in the center of the circular track, what is the area of the grassy section? Show your work.
    Radius: $127.39/2 ≈ 63.70 \text{ m}$
    Area: $3.14 \times 63.70^2 ≈ 12742.3 \text{ m}²$
    Answer: 12742.3 m²

4) Michael has a rare Canadian quarter with a diameter of 2.38 cm and a loonie with a diameter of 2.65 cm.

  1. What is the difference in circumference between the loonie and the quarter? Show your work.
    Quarter Circumference: $3.14 \times 2.38 ≈ 7.47 \text{ cm}$
    Loonie Circumference: $3.14 \times 2.65 ≈ 8.32 \text{ cm}$
    Difference: $8.32 - 7.47 = 0.85 \text{ cm}$
    Answer: 0.85 cm
  2. What is the difference in area between the top faces of the loonie and the quarter? Show your work.
    Quarter Area: $3.14 \times (1.19)^2 ≈ 4.45 \text{ cm}²$
    Loonie Area: $3.14 \times (1.325)^2 ≈ 5.51 \text{ cm}²$
    Difference: $5.51 - 4.45 = 1.06 \text{ cm}²$
    Answer: 1.06 cm²

5) A Ferris wheel at the local fair has a radius of 15 meters.

  1. How far does a person travel in one complete rotation of the Ferris wheel? Show your work.
    Formula: $C = 2\pi r$
    Calculate: $2 \times 3.14 \times 15 = 94.2 \text{ m}$
    Answer: 94.2 meters
  2. If the Ferris wheel makes 10 rotations, what is the total distance traveled by a person riding it?
    Calculate: $94.2 \times 10 = 942 \text{ m}$
    Answer: 942 meters
  3. Imagine painting the entire circular face of the Ferris wheel (excluding the seats). What is the area that needs to be painted? Show your work.
    Formula: $A = \pi r^2$
    Calculate: $3.14 \times 15^2 = 706.5 \text{ m}²$
    Answer: 706.5 m²

6) A delicious donut has a diameter of 10 cm.

  1. What is the circumference of this donut?
    Formula: $C = \pi d$
    Calculate: $3.14 \times 10 = 31.4 \text{ cm}$
    Answer: 31.4 cm
  2. If you take a bite that removes a semicircle from the donut, what is the length of the remaining outer edge?
    Half Circumference: $31.4 ÷ 2 = 15.7 \text{ cm}$
    Answer: 15.7 cm

7) Mrs. Green wants to put a decorative stone border around her circular flower bed, which has a radius of 1.5 meters.

  1. What is the length of the stone border she will need?
    Formula: $C = 2\pi r$
    Calculate: $2 \times 3.14 \times 1.5 = 9.42 \text{ m}$
    Answer: 9.42 meters
  2. If each stone costs $2.50 per meter, what will be the total cost of the border?
    Calculate: $9.42 \times 2.50 = 23.55$
    Answer: $23.55

8) An old vinyl record has a circumference of 94.2 cm.

  1. What is the diameter of the record?
    Formula: $d = C/\pi$
    Calculate: $94.2 ÷ 3.14 = 30 \text{ cm}$
    Answer: 30 cm
  2. What is the area of the playing surface of the record?
    Radius: $30/2 = 15 \text{ cm}$
    Area: $3.14 \times 15^2 = 706.5 \text{ cm}²$
    Answer: 706.5 cm²

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Educational materials for Grade 7 mathematics.