Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-C.B.5 · Level: Grade 10 Geometry
Question 1 Arc Length (2 points)
A curved garden border follows the arc s of the sector in the figure. Calculate its length exactly, then round to hundredths of an inch.
Question 2 Sector Area (2 points)
Find the area of the sector to the nearest tenth.
Question 3 Convert the Angles (2 points)
(a) Write 165° in radians, in terms of π. (1 point) (b) Write 5π/9 radians in degrees. (1 point)
Question 4 Radians from an Arc (3 points)
An arc of length 9.6 centimeters lies on a circle of radius 4 centimeters. (a) Find the central angle in radians. (1 point) (b) Find it in degrees to the nearest tenth. (1 point) (c) Find the area of the sector. (1 point)
Question 5 Radius from Area (3 points)
A sector with central angle 135° has area 96π square feet. Find the radius of the circle.
Question 6 Perimeter of a Sector (3 points)
A sector has radius 12 centimeters and central angle 1.5 radians. Find the arc length and the perimeter of the sector.
Question 7 Security Light (3 points)
A security light on a wall sweeps through a 140° sector and its beam reaches 30 feet. Find the area lit and the length of the far edge of the lit region, to the nearest tenth.
Question 8 Comparing Sectors (2 points)
Two sectors have the same central angle. Their radii are 4 inches and 10 inches. Find the ratio of the arc lengths and the ratio of the areas, larger to smaller.
