Geometry Arc Length Sectors Quiz – Free PDF

Contents

This geometry arc length sectors quiz asks 10 multiple-choice questions on arc length, sector area and radians, and each answer comes with a short explanation.

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

Score: 0 / 10

Answered: 0 / 10

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 \(r=9\text{ ft}\) and central angle \(40^{\circ}\). What is its area?

A \(9\pi\text{ ft}^{2}\)

B \(81\pi\text{ ft}^{2}\)

C \(2\pi\text{ ft}^{2}\)

D \(18\pi\text{ ft}^{2}\)

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

B 24 radians

C 3 radians

D 108 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?

A About 3.14°

B About 180°

C About 57.3°

D About 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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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

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 \(57.3^{\circ}\).