Chapter 14 - Mensuration

Eexercise - 27

  1. The total surface area of a closed right circular cylinder is 65/2cm2 and the circumference of its base is 88cm. Find the volume of the cylinder.
  2. The volume of a vessel in the form of a right circular cylinder is and its height is 7cm. Find the radius of its base.
  3. The height of a cylinder is 15cm and its curved surface area is 660 sq.cm. Find its radius.
  4. A cylindrical tank has a capacity of 6160 cu.cm. Find its depth if the diameter of its base is 28m. Also, Find the area of the inside curved surface of the tank.
  5. The volume of a right circular cylinder is 1100 cu.cm and the radius of its base is 5cm. Find its curved surface area.
  6. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
  7. 50 circular plates, each of radius 7cm and thickness 0.5cm are placed one above the other to form a solid right circular cylinder. Find the total surface area and volume of the cylinder so formed.
  8. A well of diameter 3m is dug 14m deep. The earth taken out of it has been spread evenly all around it to a width of 4m to form an embankment. Find the height of the embankment formed.
  9. The base radii of tow right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volume.
  10. If h, c and v respectively are the height, the curved surface and volume of a cone, prove that
  11. The circumference of the base of a 16 m high solid cone is 3m. Find the volume of the cone.
  12. A right circular cone of height 4 cm has a curved surface area 47.1 cm2. Find its volume .
  13. How many metres of cloth 5m wide will be required to make a conical tent, the radius of whose base is 7m and whose height is 24m?
  14. A right triangle with sides 3cm and 4cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.
  15. The radius of a sphere is 7cm. If the radius be increased by 50%, find by how much percent its volume is increased.
  16. The largest sphere is carved out of a cube of side 7cm. Find the volume of the sphere.
  17. If the surface area of sphere is 616cm2, find its volume.
  18. he volume of two spheres are in the ratio 64 : 27. Find their radii if the sum of their radii is 21cm.
  19. The circumference of the edge of a hemispherical bowl is 132cm. Find the capacity of the bowl.
  20. The internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm respectively. If the cost of painting 1cm2 of the surface area is Rs. 5.25, find the total cost of painting the vessel all over .
  21. A bucket of height 8cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3cm and 9cm respectively. Calculate:
    (i) The height of the cone of which the bucket is a part
    (ii) The volume of water which can be filled in the bucket.
    (iii) The area of copper sheet required to make the bucket.
  22. A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket
  23. The radii of the faces of a frustum of a cone are 3cm and 4cm and its height is 5 cm. Find its volume.
  24. A cone of radius 10cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base compare the volume of two parts.
  25. A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the attitude of the cone is divided by the plane.
  26. Marble of diameter 1.4cm are dropped into a cylindrical beaker of a diameter 7cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm.
  27. Sphere of diameter 5cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is 10cm. If the sphere is completely submerged, by how much will the level of water rise?
  28. A cone is 8.4cm high and the radius of its base is 2.1cm. It is melted and recast into a sphere. Find the radius of the sphere.
  29. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
  30. A conical vessel whose internal radius is 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises in the cylindrical vessel.
  31. A spherical cannon ball, 28cm in diameter is melted and cast into a right circular conical mould, the base of which is 35cm in diameter. Find the height of the cone.
  32. The radii of the internal and external surface of a metallic shell are 3cm and 5cm respectively. It is melted and recast into a solid right circular cylinder of height cm. Find the diameter of the base of the cylinder.
  33. A solid metallic sphere of diameter 21cm is melted and recasted into a number of smaller cones, each of diameter 7cm and height 3cm. Find the number of cones so formed.
  34. A solid metallic cylinder of radius 14cm and height 21cm is melted and recast into 72 equal small spheres. Find the radius of one such sphere.
  35. The diameter of a sphere is 42cm. It is melted and drawn into a cylindrical wire of 28cm diameter. Find the length of the wire.
  36. The largest sphere is carved out of a cube of side 7cm. Find the volume of the sphere.
  37. A solid sphere of radius 6cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5cm and its height is 32cm. find the uniform thickness of the cylinder.
  38. A spherical shell of lead, whose external diameter is 18cm, is melted and recast into a right circular cylinder, whose height is 8cm and diameter 12cm. Determine the internal diameter of the shell.
  39. The diameters of the internal and external surfaces of a hollow spherical shell are 6cm and 10cm respectively. If it is melted and recast into a solid cylinder of diameter 14cm, find the height of the cylinder.
  40. A hemispherical bowl of internal radius 9cm. is full of water. This water is to be filled in cylindrical bottles of diameter 3cm and height 4cm. Find the number of bottles needed to fill the whole water of the bowl.
  41. The internal and external radii of a hollow sphere are 3cm and 5cm respectively. The sphere is melted to form a solid cylinder of height cm. Find the diameter and curved surface area of the culinder.<

Answers

1. 36960cm

2. 8cm 3. 7cm
4. 10m, 880m2 5. 440sqm 6. 1 : 4
7. 3850cm 8. 1.125m 9. 9 : 25
10. 462cu m 12. 37.68cm 13. 110m
14. 3017cm3 15. 237.5% 16. 179.67cm3
17. 1437.33cm 18. 9cm, 12cm 19. 19404cm3
20. Rs. 10101.18 21. 12cm, , 22. 15cm
23. 193.8cm3 24. 1 : 7 25. 1 : 2
26. 150 27. 5/6cm 28. 2.1cm
29. 2 : 1 30. 2cm 31. 35.84cm
32. 7cm 33. 126 34. 3.5cm
35. 63 cm 36. 179.67 cm 37. 1 cm
38. 39. 8/3 cm 40. 54
41. 14 cm, 117.3cm3    
Maths by Mr. M. P. Keshari
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Subjects Maths (Part-1) by Mr. M. P. Keshari
Chapter 9 Circle
Chapter 10 Tangents to a circle
Chapter 11 Geometrical Construction
Chapter 12 Troigonometry
Chapter 13 Height and Distance
Chapter 14 Mensuration
Chapter 15 Statistics
Chapter 16 Probability
Chapter 17 Co-ordinate Geometry