Question 1: Calculate the length of an arc that represents  of the circumference of a circle with a radius of 6 cm.

Answer: 12rac34;

Question 2: What fraction of the full circumference is represented by an arc measuring 15 cm in a circle with radius 10 cm?

Answer: /3

Question 3: A circle has a radius of 8 cm. Find the length of an arc that measures  of the full circumference.

Answer: 25.13 cm

Question 4: Construct a circle with a radius of 5 cm. Mark an arc that is  of the circumference. Use the grid to illustrate this.

Answer: Constructed arc length: 6.28 cm

Question 5: A wheel of radius 0.3 m turns through an angle of 900. What fraction of the full circumference does the arc length represent?

Answer: 

Question 6: A cyclist rides along a circular track with radius 50 meters. If the cyclist travels an arc length of 100 meters, what fraction of the circumference has been covered?

Answer: 2/3

Question 7: Explain why the arc length formula   = r imes heta (in radians) is useful for finding fractions of the circumference.

Answer: Because when  is a fraction of the full circle, multiplying radius by that fraction of 2b0 gives the arc length directly.

Question 8: A sector of a circle with radius 12 cm has an arc length of 8 cm. Find the central angle in degrees.

Answer: 38.66b0

Question 9: A clock’s minute hand is 10 cm long. How much of the clock’s circumference does the minute hand sweep during 15 minutes?

Answer: /4 of the circumference

Question 10: A car tire has a radius of 0.35 meters. Calculate the length of the arc covered when the tire rotates through an angle of 1200.

Answer: 2.30 meters

Question 11: Identify and correct the mistake: A student claims that an arc measuring 8 cm in a circle with radius 4 cm represents  of the circumference.

Answer: Incorrect: arc length for  of circumference is 8, but with radius 4 cm, arc length should be 8 cm (since  =  imes 2b0 and arc length = r imes heta).