Geometry Arc Length and Sector Area Test with Point Values (PDF)

Geometry math test: Arc Length and Sector Area – Maths PDF

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This arcs sectors test for Geometry covers arc length and sector area (Common Core G-C.B.5), with a free PDF to print.

This 45-minute test checks arc length, sector area and radian measure. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Arc Length and Sector Area
Standards: G-C.B.5
Time: 45 minutes
Total: 20 points

Arcs sectors test: questions

Question 1 – Arc length [2 pts]

Sector.

Find the arc length of the sector exactly and to the nearest hundredth.

Question 2 – Sector area [2 pts]

Find the area of a sector with radius 12 and central angle 150°. Leave the answer in terms of pi.

Question 3 – Radians [3 pts]

Convert 225° to radians. (1 point)
Convert \(\frac{7\pi}{6}\) radians to degrees. (1 point)
Find the arc length when r = 9 and \(\text{theta} = \frac{2\pi}{3}\) radians. (1 point)

Question 4 – Find the radius [2 pts]

A sector with central angle 45° has area \(8\pi\). Find the radius of the circle.

Question 5 – Central angle [2 pts]

An arc of length \(5\pi\) is on a circle of radius 12. Find the central angle in degrees and in radians.

Question 6 – Sector perimeter [2 pts]

Sector.

Find the perimeter of the sector to the nearest tenth.

Question 7 – Pizza slices [2 pts]

A pizza cut into 6 equal slices.

A pizza with diameter 18 inches is cut into 6 equal slices. Find the area of one slice to the nearest tenth.

Question 8 – Wheel turn [2 pts]

A bicycle wheel has radius 14 inches. Through what angle in radians must it turn to roll forward 70 inches? How many full turns is that, to the nearest tenth?

Question 9 – Lawn [3 pts]

A garden bed is a sector with radius 20 feet and central angle 135°. Find the area of the bed and the length of the curved edge, each to the nearest tenth.

Key facts behind this arcs sectors test

Key facts

Arc length = (angle/360) x 2 pi r.
Sector area = (angle/360) x pi r squared.
180 degrees = pi radians.
In radians: arc length s = r times theta, area A = (1/2) r squared theta.
A radian is the central angle whose arc length equals the radius.

How to use this arcs sectors test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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