Question 1: A circle has a radius of 7 cm. What is the length of an arc that represents  of the circumference? Show your working.

Answer: 14 cm

Question 2: Calculate the length of an arc that is  of the circumference of a circle with radius 10 cm.

Answer: 12.56 cm

Question 3: If the entire circumference of a circle is 50π cm, what is the length of an arc measuring  of the circumference?

Answer: 25 cm

Question 4: A wheel has a radius of 15 cm. An object moves along an arc covering  of the circumference. How far does the object travel? Show all working.

Answer: 23.56 cm

Question 5: Construct a circle with radius 8 cm. Mark and shade  of the circumference on the diagram.

Answer: Student draws circle, marks arc length corresponding to  of the circumference, and shades it.

Question 6: A circular track has a radius of 20 meters. What is the length of an arc that is  of the full track?

Answer: 62.83 meters

Question 7: A pizza has a circumference of 60 cm. If a slice is  of the pizza, what is the length of the crust of that slice?

Answer: 12 cm

Question 8: A circular garden has a radius of 9 meters. Calculate the length of the arc that is  of the total circumference. Provide calculations and final answer.

Answer: 16.76 meters

Question 9: Find the arc length corresponding to  of a circle with radius 12 cm. Show your working.

Answer: 50.27 cm

Question 10: A cyclist rides along an arc covering  of a circular path with radius 25 meters. How far does the cyclist travel? Show your working.

Answer: 65.97 meters

Question 11: Identify and explain the mistake in this solution: 'Given radius = 10 cm, the arc length for  of the circle is (1/2) * 2 * 10 = 10 cm.'

Answer: Incorrect because the formula used is wrong; it should be (fraction) * 2 * radius, so for , arc length =  * 2 * 10 = 31.42 cm.