Math topic中文

Arc sector segment

arc length, sector area and area of a segment of a circle

Practice questions

  1. 1A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  2. 2In the diagram, POR is a quadrant of a circle with radius 6 cm. OR and PQ are parallel. QR is an arc of a circle with ce…
  3. 3A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  4. 4In the diagram, BA and BC are tangents to the circle with centre O. BO meets the circle at D, OA = 10 cm and BC = 28 cm.…
  5. 5The diagram shows a circle PQRST, with centre O. PV and RV are tangents to the circle and U is the intersection of PS an…
  6. 6圆锥的母线长5cm5cm，底面半径长3cm3cm，那么它的侧面展开图的圆心角是 ___ 度.
  7. 7In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  8. 8The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre P. C, D and E are point…
  9. 9The diagram shows a right circular cone cut from a solid steel sphere. Point O is the centre of the sphere with radius 1…
  10. 10The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  11. 11一个扇形的圆心角为60∘60^{\circ}，它所对的弧长为2πcm2πcm，则这个扇形的半径为 ___ cmcm．
  12. 12The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  13. 13The diagram shows a goat tied to a pole at A. The length of the rope attached to the goat is 6 m. A is due west of the c…
  14. 14The diagram shows a right-angled triangle AOB where AO = 15 cm and BO = 8 cm. P lies on AB such that OP is an arc of a c…
  15. 15The diagram shows a semicircle, centre O, radius 16 cm. Show that angle AOB = 1.287 radians, correct to 3 decimal places…
  16. 16AC is a diameter of a circle with centre O. AC=2rAC = \sqrt{2}r and AB=BCAB = BC. COB is a semi-circular arc, centre P. What p…
  17. 17A logo, as shown below, has a circle with centre O and radius 2 cm, an equilateral triangle ABC of side 5 cm and an isos…
  18. 18In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, ∠AOB = θ\theta radians, OC = 8 cm and…
  19. 19The diagram shows four identical blades of a fan, whose centre is O. Arc AB on the fan blade forms an angle of π/6\pi/6 a…
  20. 20若圆锥的底面半径为3cm3cm，母线长为5cm5cm，则这个圆锥的全面积为 ___ cm2.(cm^{2}.(结果保留π)π)
  21. 21A, B and C are points on the circle centre O and AB = BC. P is the midpoint of chord AB and Q is the midpoint of chord B…
  22. 22In the diagram, OAPB is a sector of circle with centre O and radius 9 cm. Angle AOB = 1.4 radians. C is the centre of th…
  23. 23In the diagram, OBC is the sector of a circle, centre O, and angle BOC = 60∘60^\circ. A and D are the midpoints of OB and…
  24. 24The diagram shows a triangle ABC with AB produced to D. AB=18 cmAB = 18\,\mathrm{cm}, BC=20 cmBC = 20\,\mathrm{cm}, AC=22 cmAC = 22\,\mathrm{cm}…
  25. 25AB is an arc of a circle with the centre O, ∠AOB=π/2\angle AOB = \pi/2 radians and OA=5OA = 5 cm. AC is parallel to OB and BC is…
  26. 26A chock is a block placed against a wheel or rounded object, to prevent it from moving. Jenny had to come up with a prot…
  27. 27A, B, C and D are points on the circle with centre O and radius 5 cm. AE is a tangent to the circle at A and OE is a str…
  28. 28The diagram shows a circle, centre O, radius 10 cm. AB is a chord of length 16 cm. Show that angle AOB = 1.855 radians,…
  29. 29The diagram shows two concentric circles with centre O. PQ is the diameter of the larger circle and RS is the diameter o…
  30. 30In the diagram, O is the centre of the circle through A, B, C, D and TB is the tangent at B. AC is the diameter of the c…
  31. 31A, B, C and D are points on a circle. Line PCQ is a tangent to the circle. Line QE bisects angle AEC and is parallel to…
  32. 32一个扇形占其所在圆的面积的18 \dfrac {1}{8}，则该扇形圆心角是()() A. 225∘225^{\circ} B. 45∘45^{\circ} C. 60∘60^{\circ} D. 无法计算
  33. 33The diagram, not drawn to scale, shows two concentric circles, centre O. AB and AD are tangents to the smaller circle at…
  34. 34把一个半径为22的圆分成三个扇形，使它们的圆心角的度数之比为1:3:5.(1)1:3:5.(1)求这三个扇形的圆心角的度数. (2)求这三个扇形的面积((结果保留π).\pi).
  35. 35In Diagram I below, ABCDE is a regular pentagon, centre O. OA=OB=4 cmOA = OB = 4\text{ cm}. (Diagram I and Diagram II are shown…
  36. 36A semicircle OABCDE with centre O has a radius of 4.5 cm. Chord BD has a length of 6 cm and the perimeter of minor secto…
  37. 37P, R and Q are points on the circle with centre, O. PT and QT are tangents to the circle at P and Q respectively. ∠PTQ =…
  38. 38The diagram shows a circle of radius 8 cm and centre O. The tangent to the circle at T meets OA produced at R and OB pro…
  39. 39X, Y and Z lie on a circle with centre O and radius 44 cm. Angle XOY = 2.52.5 radians. [Figure as described below] Find…
  40. 40The diagram shows the cross section of a cylinder, centre O, radius r, lying on its side. The cylinder contains water to…
  41. 41已知扇形的圆心角为120∘120^{\circ}，面积为253πcm2. \dfrac {25}{3π}cm^{2}.求扇形的弧长．