Question 1: A circle has a radius of 7 cm. Calculate its diameter.

Answer: 14

Question 2: If the radius of a circle is doubled, how does the diameter change? Explain your answer.

Answer: The diameter also doubles because it is twice the radius.

Question 3: Construct a circle with a radius of 5 units on the grid. Label the radius and diameter.

Answer: Radius = 5 units, Diameter = 10 units

Question 4: Identify the common mistake in the following statement: 'The radius of a circle is the distance from the center to any point on the circle, so the radius is always equal to the diameter.'

Answer: The radius is half the diameter, not equal.

Question 5: A circular garden has a radius of 12 meters. What is the circumference? (Use π = 3.14)

Answer: 75.36 meters

Question 6: A student measures the radius of a circle as 8 cm, but they mistakenly use the diameter formula. What is the incorrect diameter they calculate? How should they correct it?

Answer: They calculate 16 cm, which is correct for diameter when radius is 8 cm, so no correction needed. If they mistakenly used diameter formula as radius, they’d get 4 cm, which is wrong.

Question 7: Plot the circle on the grid with a radius of 4 units and mark the center and a point on the circle.

Answer: Center at (0,0), point at (4,0) for example

Question 8: Explain why the radius is a constant length in a circle, even if the circle appears larger or smaller.

Answer: Because all radii in a circle are equal by definition, regardless of the circle's size.

Question 9: A circle's radius is incorrectly estimated as 9 cm, but the diameter drawn is 15 cm. What's the mistake and the correct radius?

Answer: Mistake: The diameter should be twice the radius. Correct radius = 15 / 2 = 7.5 cm.

Question 10: A circular pool has a diameter of 10 meters. What is the radius? Show your working.

Answer: 5 meters

Question 11: If a radius is increased from 4 cm to 6 cm, by what percentage does the radius increase? How does this affect the area of the circle?

Answer: 50% increase; area increases by approximately 56.25% because area ∝ radius squared.

Question 12: Identify and correct the misconception: 'Since the radius is from the center to the circumference, it must be equal to the diameter.'

Answer: Incorrect, radius is half the diameter, not equal.