Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for an arc length and sector area quiz? Then this Geometry quiz on Arc Length, Sector Area and Radian Measure asks 10 multiple-choice questions with instant feedback. Ten multiple-choice questions on arc length, sector area, degree-radian conversions and scaling. Each explanation names the slip behind the wrong choices.
Standards: G-C.B.5 · Level: Grade 10 Geometry
What this Arc Length, Sector Area and Radian Measure quiz checks
- Arc length = (θ/360) · 2πr and sector area = (θ/360) · πr² with θ in degrees.
- Radian measure θ = s ÷ r; with radians, s = rθ and area = ½r²θ.
- 180° = π radians, so multiply degrees by π/180 to convert.
- Similar sectors with the same angle have arc lengths in the ratio of the radii.
The 10 questions of the quiz
- What is the arc length for a 90° central angle in a circle of radius 6?
- What fraction of a circle is a sector with a central angle of 45°?
- Convert 60° to radians.
- Convert 3π/2 radians to degrees.
- What is the area of the sector?
- A central angle of 2 radians intercepts an arc on a circle of radius 5. How long is the arc?
- How many degrees is 1 radian, approximately?
- Two sectors have the same central angle. The radius of the second is twice the radius of the first. How do the sector areas compare?
- What is the arc length s?
- The sector area formula in radians is
After the quiz
Missed a question? Reread the Arc Length, Sector Area and Radian Measure lesson, then take the quiz again. Next, solve the Geometry worksheet on Arc Length, Sector Area and Radian Measure, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.