Arc Length, Sector Area and Radians: Geometry Math Quiz – PDF Download
Ten quick multiple-choice questions check arc length, sector area, radian measure and degree-radian conversion. Pick the one best answer for each. The explanation after each question shows the fraction-of-a-circle idea and points out the most common slip.
GeometryCommon Core: G-C.B.5
🎯 Arc Length, Sector Area and Radians – Geometry math quiz
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Question 1
Sector with radius 6 in and central angle 60 degrees.
What is the arc length of the sector shown?
A\(\pi\text{ in}\)
B\(2\pi\text{ in}\)
C\(6\pi\text{ in}\)
D\(12\pi\text{ in}\)
Question 2
A sector has radius 6 in and central angle \(60^{\circ}\). What is its area?
A\(6\pi\text{ in}^{2}\)
B\(36\pi\text{ in}^{2}\)
C\(2\pi\text{ in}^{2}\)
D\(12\pi\text{ in}^{2}\)
Question 3
Sector with radius 10 cm and central angle 90 degrees.
What is the area of the sector shown?
A\(100\pi\text{ cm}^{2}\)
B\(25\pi\text{ cm}^{2}\)
C\(5\pi\text{ cm}^{2}\)
D\(50\pi\text{ cm}^{2}\)
Question 4
What is \(120^{\circ}\) in radians?
A\(\frac{2\pi}{3}\)
B\(\frac{3\pi}{2}\)
C\(\frac{\pi}{3}\)
D\(120\pi\)
Question 5
What is \(\frac{5\pi}{4}\) radians in degrees?
A\(150^{\circ}\)
B\(300^{\circ}\)
C\(900^{\circ}\)
D\(225^{\circ}\)
Question 6
A circle has radius 6 cm. A central angle intercepts an arc 18 cm long. What is the angle in radians?
A\(\frac{1}{3}\) radian
B24 radians
C3 radians
D108 radians
Question 7
An angle of one radian.
The angle shown has an arc exactly as long as the radius. About how many degrees is it?
AAbout 3.14°
BAbout 180°
CAbout 57.3°
DAbout 6.28°
Question 8
An arc of length \(4\pi\) in lies on a circle with radius 8 in. What is the central angle?
A\(45^{\circ}\)
B\(180^{\circ}\)
C\(120^{\circ}\)
D\(90^{\circ}\)
Question 9
A sector has radius 12 ft and central angle \(\frac{\pi}{3}\) radians. What is its area?
A\(48\pi\text{ ft}^{2}\)
B\(12\pi\text{ ft}^{2}\)
C\(24\pi\text{ ft}^{2}\)
D\(4\pi\text{ ft}^{2}\)
Question 10
A sector has radius 5 in and arc length \(\frac{5\pi}{2}\) in. What is its central angle in radians?
A\(\frac{\pi}{2}\)
B\(\frac{\pi}{4}\)
C\(\frac{5\pi}{2}\)
D\(2\pi\)
🎉 Quiz complete!
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Remember:
Arc length: \(s=\frac{\theta}{360}\cdot 2\pi r\) with \(\theta\) in degrees.
Sector area: \(A=\frac{\theta}{360}\cdot \pi r^{2}\) with \(\theta\) in degrees.
Radian measure: \(\theta=\frac{s}{r}\), so \(s=r\theta\) and \(A=\frac{1}{2}r^{2}\theta\).
\(180^{\circ}=\pi\) radians, and one radian is about \(57.3^{\circ}\).
