Geometry Arc Length Sectors Test – Free PDF

Contents

This geometry arc length sectors test checks arc length, sector area and radians in 45 minutes, with 9 questions for a total of 20 points.

This 45-minute test has 9 questions worth 20 points. It covers arc length, sector area, radian measure and conversions between degrees and radians. Calculators are allowed. Show the work, give exact answers in terms of \(\pi\) when asked, and include units.

Test information

Grade: Geometry
Chapter: Arc Length, Sector Area and Radians
Common Core: G-C.B.5
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 2 pts)

Geometry Arc Length Sectors Test: questions 1–5

Question 1: Arc length (2 points)

Sector with radius 15 in and central angle 48 degrees.

Find the length of the arc in the sector shown. Give the exact length and a decimal rounded to the nearest hundredth.

Question 2: Sector area (2 points)

Sector with radius 9 cm and central angle 200 degrees.

Find the area of the sector shown. Give the exact area and a decimal rounded to the nearest hundredth.

Question 3: Angle and area from arc (3 points)

Arc of length 8π in on a circle of radius 12 in.

An arc of length \(8\pi\) in lies on a circle with radius 12 in.

Find the central angle in degrees. (1 point)
Find the area of the sector with that central angle. Give the exact area and a decimal rounded to the nearest hundredth. (2 points)

Question 4: Radian measure (2 points)

A central angle in a circle of radius 7 cm intercepts an arc 21 cm long. Find the angle in radians, and explain what a measure of 1 radian means.

Question 5: Degrees to radians (2 points)

Convert each angle to radians. Give exact answers in terms of \(\pi\).

\(135^{\circ}\)
\(300^{\circ}\)
\(20^{\circ}\)

Geometry Arc Length Sectors Test: questions 6–9

Question 6: Radians to degrees (2 points)

Convert each angle to degrees.

\(\frac{11\pi}{6}\) radians
\(\frac{3\pi}{2}\) radians
\(\frac{2\pi}{5}\) radians

Question 7: Radius from sector area (3 points)

A sector with a central angle of \(150^{\circ}\) has an area of \(60\pi\text{ ft}^{2}\).

Find the radius of the circle. (2 points)
Find the length of the arc of this sector. Give the exact length. (1 point)

Question 8: Windshield wiper (2 points)

A lawn sprinkler sprays water out to a distance of 15 ft. In one sweep, it turns through \(140^{\circ}\). Find the area of lawn that the water reaches in one sweep. Round to the nearest square foot.