Question 1: Calculate the circumference of a circle with a radius of 7 cm.

Answer: 43.96

Question 2: A circle has a diameter of 20 cm. Find its circumference.

Answer: 62.83

Question 3: What is the radius of a circle if its circumference is 31.4 cm? (Use π ≈ 3.14)

Answer: 5

Question 1: A bike wheel has a radius of 30 cm. Calculate its circumference. Then, explain why using the diameter instead of the radius in the formula might lead to an error if students forget the relationship between diameter and radius.

Answer: Circumference = 2 × 3.14 × 30 = 188.4 cm. Using diameter directly without halving could lead to incorrect calculations if students confuse D and r.

Question 2: A circular garden has a circumference of 62.8 meters. Find its radius. Show your working, and consider what common mistake students might make when using the formula.

Answer: r = 62.8 / (2 × 3.14) = 10 m

Question 1: A circular track has a radius of 50 meters. Calculate how far a runner will travel if they complete 3 laps.

Answer: Distance = 3 × 2 × 3.14 × 50 = 942 meters

Question 2: A manufacturer designs circular tables with a radius of 1.2 meters. If a table's circumference is mistakenly calculated as 7 meters instead of the correct value, identify the error and correct it.

Answer: Incorrect: 2 × 3.14 × 1.2 ≈ 7.54 meters. Mistake: Used π correctly but perhaps approximated or miscalculated.

Question 1: A circle has a circumference of 100 meters. If the radius is increased by 25%, what is the new circumference? Show your working and discuss the proportional relationship.

Answer: New radius = 1.25 × original r Original r = 100 / (2 × 3.14) ≈ 15.92 m New r ≈ 19.9 m New circumference ≈ 2 × 3.14 × 19.9 ≈ 125.0 m

Question 2: Design a problem where students must determine whether a given diagram showing a radius of 8 cm and diameter of 16 cm is correct. Based on the diagram, identify and explain any misconceptions.

Answer: The diagram is correct since diameter = 2 × radius = 16 cm. Misconception: Assuming radius and diameter are equal or mixing up their values.

Question 1: A student calculates the circumference of a circle with radius 10 cm as 31.4 cm, claiming they used π ≈ 3.14. Is their answer correct? If not, what is the correct value? Identify if they made a mistake and explain.

Answer: Correct: 2 × 3.14 × 10 = 62.8 cm. Mistake: They only multiplied once or used wrong approximation.

Question 2: Identify and correct the mistake in calculating the circumference of a circle with radius 5 meters, where a student states the answer as 15.7 meters.

Answer: Incorrect. Correct: 2 × 3.14 × 5 = 31.4 meters. Misconception: Using diameter instead of radius or incorrect π value.