Arc Length and Sector Area: Radians and Formulas in Action

A pizza has a radius of 10 inches. If a slice of pizza represents a central angle of 60 degrees, what is the arc length of the slice? (Use the formula: Arc Length = r * θ, where θ is in radians.)

• 10π/3 inches

• 5π inches

• 20 inches

• 15π/4 inches

A circular garden has a radius of 5 meters. If a sector of the garden has a central angle of 90 degrees, what is the area of that sector? (Use the formula: Area = 0.5 * r^2 * θ, where θ is in radians.)

• 15π square meters

• 20π square meters

• 12.5π square meters

• 10π square meters

Convert 120 degrees to radians. Then, if a circular track has a radius of 15 meters, calculate the arc length corresponding to this angle.

• 5π meters

• 30π meters

• 10π meters

• 15 meters

A clock's minute hand is 12 cm long. What is the length of the arc traced by the minute hand in 15 minutes? (Assume the minute hand moves 360 degrees in 60 minutes.)

• 9.42 cm

• 12.56 cm

• 6.28 cm

• 15.70 cm

A sector of a circle has an area of 25π square centimeters and a radius of 10 cm. What is the central angle of the sector in degrees? (Use the formula: Area = 0.5 * r^2 * θ.)

• 45 degrees

• 180 degrees

• 90 degrees

• 120 degrees

A circular swimming pool has a radius of 8 meters. If you want to paint a sector of the pool that has a central angle of 45 degrees, how much area will you need to paint?

• 4π square meters

• 8π square meters

• 16π square meters

• 2π square meters

If a wheel has a radius of 0.5 meters and makes a complete rotation, what is the distance traveled along the circumference? (Use the formula: Circumference = 2 * π * r.)

• 0.5 meters

• 6.28 meters

• 3.14 meters

• 1.57 meters

A sector of a circle has a radius of 7 cm and a central angle of 135 degrees. Calculate the arc length of the sector.

• 25.30 cm

• 16.54 cm

• 10.50 cm

• 20.00 cm

Convert 240 degrees to radians and find the area of the sector with a radius of 4 meters corresponding to this angle.

• 32π/3 square meters

• 24π/5 square meters

• 40 square meters

• 16π square meters

A bicycle wheel has a radius of 0.6 meters. If the wheel rotates through an angle of 150 degrees, what is the length of the arc that the wheel covers?

• 0.75 meters

• 1.57 meters

• 2.10 meters

• 1.25 meters