Arc Length, Sector Area and Radians: Geometry Math Test – PDF Download

Question 1: Arc length (2 points)

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)

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)

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

1. Find the central angle in degrees. (1 point)
2. 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 \(\pi\).

1. \(135^{\circ}\)
2. \(300^{\circ}\)
3. \(20^{\circ}\)

Question 6: Radians to degrees (2 points)

Convert each angle to degrees.

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

Question 7: Radius from sector area (3 points)

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

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

Question 8: Windshield wiper (2 points)

A windshield wiper blade pivots at one end, and the blade is 24 in long. In one sweep it turns through \(110^{\circ}\). Find the area of the windshield region that the blade sweeps. Round to the nearest square inch.

Question 9: Arc and area in radians (2 points)

A sector has radius 10 in and central angle \(\frac{2\pi}{5}\) radians. Find the arc length and the area of the sector. Give exact answers.

⬇ Download the Geometry Arc Length, Sector Area and Radians test (PDF, 82 KB)

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