# Circular sector - examples

1. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
2. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
3. Circle arc Circle segment has a circumference of 72.95 cm and 1386.14 cm2 area. Calculate the radius of the circle and size of central angle.
4. Radians Convert 270° to radians. Write result as multiple of number π.
5. Arc Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
6. Circular pool The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
7. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
8. Estate Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?
9. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
10. Circle section Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
11. Circle and angle What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
12. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
13. Circular sector I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
14. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
15. Arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
16. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
17. Circle arc Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
18. Bridge The bridge arc has a span 235 m and height 3 m. Calculate the radius of the circle arc of this bridge.
19. Circle sector Circular sector with a central angle 80 ° has area 1257 cm2. Calculate its radius r.
20. Field with vegetables Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?

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