Area and Circumference of Circle- WS2

Circle Problems: Area & Circumference Practice (Part 2) - The Study Zone

Circle Problems: Area & Circumference Practice (Part 2)

9) A student is using a hula hoop with a diameter of 80 cm.

  1. How many meters does the hula hoop travel in one complete rotation?
    Convert to meters: 80 cm = 0.8 m
    Circumference: $3.14 \times 0.8 = 2.512 \text{ m}$
    Answer: 2.512 meters
  2. If the student spins the hula hoop 25 times, what is the total distance the edge of the hoop travels?
    Calculate: $2.512 \times 25 = 62.8 \text{ m}$
    Answer: 62.8 meters

10) After a rain shower, a circular puddle forms with a radius of 0.75 meters.

  1. What is the area covered by the puddle?
    Formula: $A = \pi r^2$
    Calculate: $3.14 \times 0.75^2 ≈ 1.77 \text{ m}²$
    Answer: 1.77 m²
  2. If the puddle evaporates at a rate of 0.1 m² per hour, how long will it take for the entire puddle to disappear?
    Time: $1.77 ÷ 0.1 = 17.7 \text{ hours}$
    Answer: 17.7 hours

11) A circular target has a diameter of 60 cm. The bullseye in the center has a diameter of 10 cm.

  1. What is the area of the entire target?
    Radius: 30 cm
    Area: $3.14 \times 30^2 = 2826 \text{ cm}²$
    Answer: 2826 cm²
  2. What is the area of the bullseye?
    Radius: 5 cm
    Area: $3.14 \times 5^2 = 78.5 \text{ cm}²$
    Answer: 78.5 cm²
  3. What is the area of the target outside the bullseye?
    Calculate: $2826 - 78.5 = 2747.5 \text{ cm}²$
    Answer: 2747.5 cm²

12) The wheel of a bicycle has a diameter of 66 cm.

  1. What is the circumference of the bicycle wheel?
    Formula: $C = \pi d$
    Calculate: $3.14 \times 66 = 207.24 \text{ cm}$
    Answer: 207.24 cm
  2. How many rotations will the wheel make if the bicycle travels a distance of 100 meters? (Round to the nearest whole number).
    Convert: 100 m = 10000 cm
    Rotations: $10000 ÷ 207.24 ≈ 48.25$
    Answer: 48 rotations

13) A circular table has a diameter of 1.2 meters. A tablecloth hangs 20 cm over the edge all around.

  1. What is the diameter of the tablecloth?
    Overhang: 20 cm = 0.2 m
    Total diameter: $1.2 + (0.2 \times 2) = 1.6 \text{ m}$
    Answer: 1.6 meters
  2. What is the area of the tablecloth?
    Radius: $1.6/2 = 0.8 \text{ m}$
    Area: $3.14 \times 0.8^2 ≈ 2.01 \text{ m}²$
    Answer: 2.01 m²

14) A nickel has a radius of 1.06 cm, and a dime has a radius of 0.94 cm.

  1. What is the circumference of the nickel?
    Formula: $C = 2\pi r$
    Calculate: $2 \times 3.14 \times 1.06 ≈ 6.66 \text{ cm}$
    Answer: 6.66 cm
  2. What is the circumference of the dime?
    Calculate: $2 \times 3.14 \times 0.94 ≈ 5.90 \text{ cm}$
    Answer: 5.90 cm
  3. What is the difference in their circumferences?
    Difference: $6.66 - 5.90 = 0.76 \text{ cm}$
    Answer: 0.76 cm

15) A sprinkler in the center of a circular lawn with a radius of 8 meters rotates and waters a circular area with a radius of 5 meters.

  1. What is the area of the lawn that is watered by the sprinkler?
    Formula: $A = \pi r^2$
    Calculate: $3.14 \times 5^2 = 78.5 \text{ m}²$
    Answer: 78.5 m²
  2. What is the area of the lawn that is not watered by the sprinkler?
    Total Area: $3.14 \times 8^2 = 200.96 \text{ m}²$
    Unwatered: $200.96 - 78.5 = 122.46 \text{ m}²$
    Answer: 122.46 m²

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Educational materials for Grade 7 mathematics.