Area of Circle, Sector and Segment

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Derrick Moody
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1. Find the circumference and area of a circle of radius 10.5 cm. 2. Find the area of a circle whose circumference is 52.8 cm. 3. Afield is in the form of a circle.

The same wire is bent, in the form of a circle. Find the area of the circle. 5. A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form.

2 1. Find the circumference and area of a circle of radius 10.5 cm. 2. Find the area of a circle whose circumference is 52.8 cm. 3. Afield is in the form of a circle. The cost of ploughing the field at Rs 1.50 per m 2 is Rs 55. Find the cost of fencing the field at Rs 8.50 per metre. 4. A steel wire, when bent in the form of a square, encloses an area of 121 sq cm. The same wire is bent, in the form of a circle. Find the area of the circle. 5. A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form. Determine the length of the side of the square. 6. A circular park. 42 m in diameter, has a path 3.5 m wide running round it. on the outside. Find the cost, of gravelling the. path at Rs 4 per m 2. A road which is m wide surrounds a circular park whose circumference is 352 m. Find the area of the road. 8. A racetrack is in the form, of a ring whose inner and outer circumferences are 43 m and 503 m respectively. Find the width of the track and also its area. 9. If the. perimeter of a semicircular protractor is 36 cm, find its diameter. 10. A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel. 11. The diameter of the wheels of a bus is 140 cm. How many revolutions per- minute must a wheel make in order to move at a speed of 66 km per hour? 12. Two circles touch externally. The sum of their areas is 1 Hire sq cm and the distance between their centres is 14 cm. Find the radii of the circles. 13. Two circles touch internally. The sum of their areas is (116n:) cm 2 and the distance betiveen their centres is 6 cm. Find the radii of the circles. 14. A paper is in the.form of a rectangle ABCD in Whieh AB =1 8 c m and BC= 1 4 c m. A semicircular portion with BC as diameter is cut off. Find the area of the remaining paper. 15. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first?132 m2 16. Two circles touch externally. The sum of their areas is 130 sq. cm and the distance between their centres is 14 cm. Find the radii of the circles. 11cm and 3 cm 2 P a g e m a t h s c l a s s x

1. A wire when bent in the form of an equilateral triangle encloses an area of 121 3 cm 2. If the same wire is bent in the form of a circle, find the area of the circle. 346.5 18.

A wheel of diameter 42 cm, makes 240 revolutions per minute. Find : (i) the total distance covered by The wheel in one minute. (ii) the speed of the wheel in km/hr. 316.8m and 19.008 km/h 20.

3 1. A wire when bent in the form of an equilateral triangle encloses an area of cm 2. If the same wire is bent in the form of a circle, find the area of the circle The area enclosed between the two concentric circles is 0 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle A wheel of diameter 42 cm, makes 240 revolutions per minute. Find : (i) the total distance covered by The wheel in one minute. (ii) the speed of the wheel in km/hr m and km/h 20. An arc of length 20 cm subtends an angle of 144 at the centre of the circle. Find radius of circle.25cm 21. The perimeter of a sector of a circle of radius 5. m is 2.2 m. Find the area of the sector m2 22. In the given figure, the length of the minor arc is /24 of the circumference of the circle. Find : (i) <AOB (ii) If it is given that the circumference of the circle is 132 cm, find the length of the minor arc AB and the radius of the circle.105, 38.5, 21 3 marks type Questions. 23. In figure 1, find the area of the shaded region. (Use π =3.14) {ans cm 2} 24. A playground in the form of a rectangle having semicircles on the shorter sides as shown in fig. 2. Find its area when the length of the rectangular portion is 80 m and the breadth is 42 m. {Ans. 446 cm 2 ) 25. A toy is in the form of a cone mounted on a hemisphere of common base radius cm. the total height of the toy is 31 cm. find the total surface area of the toy. {ANS 858 cm 2} 26. Four equal circles are described about four corners of a square so that each touches two of the others, as shown in fig. Find the area of the shaded region, each side of the square measuring 14cm. (take use π= 22 ) {Ans. 42 Sq. cm} 2. In figure PQ=24cm, PR = cm and o is the centre of the circle. Find the area of shaded region (take use π=3.14){ans cm 2 } 3 P a g e m a t h s c l a s s x

28. 2 cubes each of volume 64cm 3 are joined end to end. Find the surface area of the resulting cuboid. 29. The length of the minute hand of a clock is 14cm.

4 28. 2 cubes each of volume 64cm 3 are joined end to end. Find the surface area of the resulting cuboid. 29. The length of the minute hand of a clock is 14cm. find the area swept by the minute hand in 5 minutes. (Use π= 22 ) {ANS= 51.3 cm 2 }. 30. Find the area of the shaded region in fig. if AC= 24cm, BC = 10cm and o is the centre of the circle. Use π = 22 [ANS cm 2 } 31. In figure, find the area of the shaded region, if ABCD is rectangle with AB =80 cm and BC = 0 cm. Angle AED =90 0 and DE = 42 cm and a semicircle is drawn with BC as a diameter. Take π= 22 {ANS= 2499cm2 } 32. The radius of the base and the height of a solid right circular cylinder are in the ratio2:3 and its volume are 161. Cm 3. find the total surface area of the cylinder. {Use π= 22 } 33. A square park has each side of 100m. At each corner of the park, there is a flower-bed in the form of a quadrant of radius 14cm as shown in fig.4. Find the area of the remaining part of the park. {Use π= 22 }. (Ans Sq. m.) 34. A room is 8m long, 4.5 m wide high. It has one door 1.4 m wide and 2m high with a semicircular ventilator as shown in fig. and two rectangular windows 2m by 1.5m each. Find the cost of white-washing the inner four walls of the room rate of rs.10per sq. m.. {Use π= 22 }. (Ans Rs ) Q A cylinder of radius 12 cm contains water to depth of 20cm. a spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.5 cm. find the radius of the ball.. {Use π= 22 }. (Ans. 4) 4 P a g e m a t h s c l a s s x

36. The short and long hands of a clock are 4cm and 6cm long respectively. Find the sum of the distances travelled by their tips in two days.. {Use π= 22 }. (Ans 1910.86 cm ) 3.

5 36. The short and long hands of a clock are 4cm and 6cm long respectively. Find the sum of the distances travelled by their tips in two days.. {Use π= 22 }. (Ans cm ) 3. A hemispherical bowl of internal diameter 36cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. find the number of bottles needed to empty the bowl. (ans. 2) 38. Find the area of the shaded region in fig. where ABCD is a square of side 14cm. (Ans. 42) 39. The area of an equilateral triangle is 49route3 cm 2. Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circle. {Use π= 22 }. 4 marks type Questions. 40. A bucket is made up of metal sheet is in the form of a frustum of a cone, its depth is 24cm and the diameters of the top and bottom are 30cm and 10cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs.20 per liter and the cost of the metal sheet used, if it cost Rs.10 per 100cm 2. {Use π= 22 }. (Ans. Rs ) 41. A sphere of diameter 12 cm is dropped in a right circular cylinder vessel partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 32/9cm. find the diameter of the cylindrical vessel. (Ans. 10 cm) 42. A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14m and 26m respectively, the height of the frustum be 8m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal). (Ans approx.) 43. From a solid cylinder whose height is 8cm and radius 6 cm, a conical cavity of height 8cm and of base radius 6cm, hollowed out. Find the volume of the remaining solid correct to two places of decimal. Also find the total surface area of the remaining solid. (Use π =3.1416) (Ans cm 3 ) 44. A juice seller serves his customers using a glass,the inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity. (Use π =3.14) (Ans cm 3 ) 5 P a g e m a t h s c l a s s x

45. A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 3216/cm 3. The radii of its lower and upper circular ends are 8cm and 20cm respectively.

6 45. A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 3216/cm 3. The radii of its lower and upper circular ends are 8cm and 20cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs.1.40 per square centimeter. {Use π= 22 }. (Ans. Rs ) 46. A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemispherical is equal to the edge of the cube. Determine the volume and total surface area of the remaining block. (Ans cm 2 ) 4. Find the area of the shaded region in fig where arcs drawn with centre s A, B,C and D interest in pairs at midpoints P, Q,R And S of the sides AB, BC, CD, DA respectively of a square ABCD, where the length of each side of square is 14cm {Use π= 22 }. (Ans. 42 cm2.) 48. A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21cm and 40cm respectively, and the height of cone is 15cm, then find the total surface area of the toy. (Use π =3.14) (Ans cm The length and breadth of rectangular piece of paper are 28cm and 14cm respectively. A semi-circular portion is cut off from the breadth s side and a semi-circular portion is added on length s side as shown fig. find the area of the shaded region.{use π= 22 }. (623 cm2 ) 50. A steel wire, when bent in the form of a square, encloses an area of 121 sq cm. the same wire is bent in the form of a circle. Find the area of the circle. 51. A wire is looped in the form of a circle of radius 28 cm. it is rebent into a square form. Determine the length of the side of the square. 6 P a g e m a t h s c l a s s x

52. A road which is m wide surrounds a circular park whose circumference is 352 m. find the area of the road. 53. If the perimeter of a semicircular protractor is 36 cm, find its diameter. 54.

7 52. A road which is m wide surrounds a circular park whose circumference is 352 m. find the area of the road. 53. If the perimeter of a semicircular protractor is 36 cm, find its diameter. 54. A bicycle wheel makes 5000 revolution in moving 11 km. find the diameter of the wheel. 55. The area of the sector of a circle of radius 10.5 m is 69.3 cm 2. Find the central angle of the sector. 56. A pendulum swings through an angle of 30 and describes an arc 8.8 cm in length. Find the length of the pendulum. 5. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days. Take π = Find the area of a right angle triangle, if the radius of its circumcircle is 2.5 cm and the altitude drawn to the hypotenuses is 2 cm long. 59. Two circle touch externally. The sum of their area is 130 π sq cm and the distance between their centres is 14 cm. find the radii of the circles. 60. In the given figure, OABC is rhombus whose three vertices A, B, C lie on a circle of radius 10 cm. find the area of the rhombus. Take Three horses are lethered with meter long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed. 63. The circumference of a circle exceeds its diameter by 16.8 cm. find the circumference of the circle. 64. The inner circumference of a circular track is 440 m, and the tract is 14 m wide. Calculate the cost of leveling the track at 25 paisa/m 2 also find the cost of fencing the outer boundary of the tract at Rs 5 per metre. 65. PQRS is diameter of a circle of radius 6 cm. the lengths PQ, QR and RS are equal semicircles are drawn with PQ and FQSS as diameters, as shown in the given figure. If PS = 12 cm, find the perimeter and area of the shaded regions. Take π = P a g e m a t h s c l a s s x

66. In the given figure, OPQR is a rhombus, three of whose vertices les on a circle with centre O. if the area of the (i) (ii) rhombus is 32 cm 2 find the radius of the circle. 6 marks 6.

8 66. In the given figure, OPQR is a rhombus, three of whose vertices les on a circle with centre O. if the area of the (i) (ii) rhombus is 32 cm 2 find the radius of the circle. 6 marks 6. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find : (i) Area of the minor sector (ii) Area of the minor segment 8.5cm2, , cm2 (iii) Area of major sector (iv) Area of major segment ( use = 3.14 ) 68. A chord of a circle of radius 12 cm subtends an angle of 120 at the centre. Find the area of the corresponding segment of the circle. [use = 3.14, 3 = 1.3] [88.44 cm2] 69. In the given figure 1, ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region. [16π -12 3] 0. The following figure 2 shows a rectangle ABCD inscribed in a circle. If AB = 8 cm and BC = 6 cm, find the area of the circle not included in the rectangle. If diameter of the circle is 25 cm and BC = 15 cm, find the area of the circle not included in the given rectangle.[ cm2 ], A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi circular portion with BC as diameter is cut off. Find the area of the remaining part 203 cm2 2. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal, semi-circles are drawn on PQ and QS as diameters as shown in figure3. Find the perimeter and area of the shaded region.12π 3. In the following figure 4, ABC is an equilateral triangle. Circles are drawn with vertices of the triangle ABC as centers so that every circle touches the remaining two. If the perimeter of the triangle ABC is 84 cm. 4. Find: (i) area of sector, inside the triangle, of each circle. (ii) area of the triangle which is not included in the circle. [use = 3.14, 3 = 1.3]102.5, 31.3 Fig 4 Fig 1 Fig 2 Fig 3 8 P a g e m a t h s c l a s s x

5. Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area, enclosed between the circles is 24/cm 2. Find radius of the each circle.

9 5. Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area, enclosed between the circles is 24/cm 2. Find radius of the each circle.2 6. Three horses are tethered with m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed fig 6.[ m2, 259 m2]. In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find area of the shaded region.0 8. A circle has been inscribed in a square of side 4 cm. Determine the left out area. What will be the left out area of the circle if a square is inscribed in the circle, fig? [use = 3.14] [3. 44Cm2] 9. In given Fig.8, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.[ Fig 6 fig fig 8 9 P a g e m a t h s c l a s s x

13. Surface Areas and Volumes. Q 2 The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions?

13. Surface Areas and Volumes. Q 2 The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions? 13. Surface Areas and Volumes Q 1 Find the area enclosed between two concentric circles of radii 4 cm and 3 cm. Q 2 The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover