Circular sector practice problems
A circular sector is the region enclosed by two radii and the arc between them, resembling a "slice of pie" from a circle. The sector is characterized by the central angle θ (in radians or degrees) and the radius r. The arc length is s = rθ (when θ is in radians) or s = (πrθ)/180 (when in degrees). The area of a sector is A = (1/2)r²θ (radians) or A = (πr²θ)/360 (degrees). Special cases include the semicircle (θ = π or 180°) and quadrant (θ = π/2 or 90°). Sectors appear in applications involving circular motion, pie charts, pendulums, and angular measurements in physics and engineering.Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.
Number of problems found: 72
- Circle graph
Erica surveyed students at her school about their favorite type of music. She made a circle graph to show the results. The central angle for the section of the graph that represents country music measures 72°. If 45 classmates chose the country as their f - A goat 2
As shown, a goat is tied at one corner of a rectangular shed by a 5-meter-long rope. The shed measures 3 m by 2 m and is surrounded by grassland. What is the area of the grassland in which the goat can graze? Give your answer to the nearest m². - Minute hand area
How big is the area of the circular cutout described by the minute hand 14 cm long in 40 minutes? - Trajectory
Nelka holds a dumbbell in her hand at arm's length. Then she lifts it by bending her arm only at the elbow, making an angle of 135°. The exercise ends with the dumbbell lowering along the same path. What is the length of the trajectory the dumbbell follow - Disc
The circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc? - Circular dragon
The dragon has the shape of a circular section with a central angle of 40° and a radius of 35 cm. How much paper do we need to make if 10% is added to the curved ones? - Clock path
The large hand on the clock is 14 cm long. What path will the tip of the hand describe in 35 minutes? - Circle and angle
What is the length of the arc of a circle with radius r = 432 dm with central angle 0.53 rad? - Circle arc + section Calculate the length of the arc of a circle and the volume of a circular section if the circle's radius is 8.3 centimeters and the central angle alpha=104 degrees.
- Radians
Convert 90° to radians. Write the result as a multiple of the number π. - Circular section area
Calculate the area of a circular section given by an angle of 220 degrees if the circle's radius is 20cm. Round the result to cm2 - Arc
What area of a circle occupied the flowers planted in the arc of a circle with a radius 3 m with a central angle of 45°? - Arc
The circle arc corresponding to the angle is 357° is 18 dm long. What is the length of the entire circle? - Sector
The perimeter of a circular sector with an angle 0.7 rad is 53 cm. Determine the radius of the circle from which the sector comes. - Length of the arc
What is the arc length of a circle k (S, r=68mm), which belongs to a central angle of 78°? - Irrigation sprinkler
The irrigation sprinkler can twist at an angle of 320° and reach 12 meters. Which area can you irrigate? - Quadrant II
Calculate the radius of the quadrant, which area is equal to the area of the circle with radius r = 15 cm. - Quarter circular
The wire hooked around the perimeter of the quarter-circular arc has a length of 14π+56. Determine the radius of the circle arc. - Estate
Semicircle estate must be a fence. The straight section has a 32 meters long fence. How many meters of the fence should we buy? - The central
The central angle of a sector is 30°, and the radius is 15 m. Determine its perimeter.
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