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: 71
- 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
What is the area of the circular cutout described by the minute hand 14 cm long in 40 minutes? - 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? - Disc
The circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc? - Clock path
The minute hand on a clock is 14 cm long. What distance does the tip of the hand travel in 35 minutes? - Radians
Convert 90° to radians. Write the result as a multiple of π. - Circle and angle
What is the arc length of a circle with radius r = 432 dm corresponding to a central angle of 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. - Arc
What area is occupied by flowers planted in a circular sector with a radius of 3 m and a central angle of 45°? - Arc
The arc of a circle corresponding to a central angle of 357° is 18 dm long. What is the circumference of the entire circle? - Circular section area
Calculate the area of a circular section given by an angle of 220 degrees if the circle's radius is 20 cm. Round the result to cm2 - Estate
A semicircular plot of land is to be fenced. The straight section of the fence is 32 metres long. How many metres of fencing in total need to be bought? - Irrigation sprinkler
The irrigation sprinkler can twist at an angle of 320° and reach 12 meters. Which area can you irrigate? - 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. - 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. - The central
A circular sector has a central angle of 30° and a radius of 15 m. Determine its perimeter. - Length of the arc
What is the arc length of a circle k (S, r=68 mm), which belongs to a central angle of 78°? - Arc
The length of the circle is 13, and the arc length of the circle is 5. What is the magnitude of the angle of this arc?
Do you have unsolved math question and you need help? Ask a question, and we will try to solve it. We solve math question.
