1. A right triangle with sides 5 cm, 12 cm and 13 cm is rotated about the side 5 cm to form a cone. The volume of the cone so formed is (Take π = 22/7):
a) 440 cm³
b) 880 cm³
c) 220 cm³
d) 660 cm³
2. The ratio of the volumes of two cones is 4 : 9 and the ratio of the radii of their bases is 2 : 3. The ratio of their heights is:
a) 1 : 1
b) 2 : 3
c) 3 : 2
d) 4 : 3
3. If the radius of a cone is tripled while its height remains the same, the ratio of the volume of the original cone to that of the new cone will be:
a) 1 : 3
b) 1 : 6
c) 1 : 9
d) 3 : 1
4. If the height of a cone is tripled and its radius remains unchanged, the ratio of the volume of the new cone to that of the original cone will be:
a) 1 : 3
b) 3 : 1
c) 9 : 1
d) 1 : 9
5. If the radius of both a cone and a sphere is 3 cm and their volumes are equal, the slant height of the cone is:
a) 5 cm
b) 6 cm
c) 10 cm
d) 4 cm
6. A cone of height 10 cm and base diameter 10 cm is carved out of a wooden sphere of radius 5 cm. The percentage of wasted wood is:
a) 50%
b) 66⅔%
c) 75%
d) 80%
7. In a right circular cone, the radius of its base is 8 cm and its height is 24 cm. A cross-section is made through the midpoint of the height parallel to the base. The volume of the upper portion is:
a) 64π cm³
b) 96π cm³
c) 128π cm³
d) 256π cm³
8. If the area of the base of a cone is 616 cm² and the area of its curved surface is 880 cm², then its volume (in cm³) is (Use π = 22/7):
a) 1232 cm³
b) 2464 cm³
c) 1848 cm³
d) 3080 cm³
9. The volumes of two cones are in the ratio 4 : 9 and the diameters of their bases are in the ratio 2 : 3. The ratio of their heights is:
a) 1 : 1
b) 2 : 3
c) 3 : 2
d) 4 : 3
10. The height of a cone is 24 cm. A small cone is cut off at the top by a plane parallel to its base. If the volume of the small cone is 1/8 of the volume of the original cone, at what height above the base is the section made?
a) 6 cm
b) 12 cm
c) 16 cm
d) 18 cm
11. The radius of the base and height of a right circular cone are in the ratio 3 : 4. If the volume of the cone is 616 cm³, then the slant height (in cm) of the cone is:
(Use π = 22/7)
a) 5 cm
b) 10 cm
c) 15 cm
d) 25 cm
12. The ratio of the radii of two cones is 2 : 5 and the ratio of their heights is 5 : 4. The ratio of their volumes is:
a) 1 : 5
b) 4 : 25
c) 5 : 4
d) 25 : 4
13. A right circular cone is divided into three solids by two planes parallel to its base which trisect the altitude. If the volumes of the three solids from top to bottom are v₁, v₂ and v₃ respectively, then v₁ : v₂ : v₃ is:
a) 1 : 7 : 19
b) 1 : 8 : 27
c) 3 : 5 : 7
d) 1 : 6 : 12
14. The radii of the circular ends of a truncated conical bucket are 21 cm and 14 cm, and its height is 12 cm. Find the capacity of the bucket in cubic centimetres. (Take π = 22/7)
a) 12320 cm³
b) 11088 cm³
c) 9856 cm³
d) 15400 cm³
15. The ratio of the height to the diameter of a right circular cone is 2 : 1. If its volume is 2464 cm³, then (Take π = 22/7) the height of the cone is:
a) 14 cm
b) 21 cm
c) 28 cm
d) 35 cm
16. The heights of two cones are in the ratio 2 : 5 and the diameters of their bases are in the ratio 3 : 4. The ratio of their volumes is:
a) 9 : 40
b) 18 : 80
c) 8 : 15
d) 27 : 80
17. The circumference of the base of a solid cone of height 21 cm is 44 cm. What is the volume of the cone (in cm³)?
(Take π = 22/7)
a) 462 cm³
b) 308 cm³
c) 154 cm³
d) 616 cm
18. The circumference of the base of a right circular cone is 44 cm. If the height of the cone is 24 cm, then its volume is: (Take π = 22/7)
a) 4928 cm³
b) 1232 cm³
c) 2464 cm³
d) 3696 cm³
19. If the volumes of two right circular cones are in the ratio 9 : 4 and the ratios of the diameters of their bases is 3 : 2, then the ratio of their heights is:
a) 1 : 1
b) 2 : 1
c) 3 : 2
d) 4 : 3
20. The volume of a conical tent is 616 m³ and the area of its base is 154 m².
Find the length of the canvas required to build the tent, if the canvas is 2 m wide.
a) 55 m
b) 66 m
c) 77 m
d) 88 m
21. The ratio of the diameters of two right circular cones of equal height is 5 : 6. The ratio of their volumes is:
a) 25 : 36
b) 125 : 216
c) 5 : 6
d) 1 : 1
22. If the ratio of the radii of two right circular cones of equal height is 2 : 5, then the ratio of their volumes will be:
a) 2 : 5
b) 4 : 25
c) 8 : 125
d) 16 : 25
23. The ratio of the volume of a cube to that of a hemisphere which fits exactly inside the cube (its diameter equal to the side of the cube) is:
a) 3 : 2
b) 6 : 1
c) 3 : 1
d) 2 : 1
24. The heights of a cylinder and a cone are in the ratio 3 : 2 and the radii of their bases are in the ratio 2 : 3. The ratio of their volumes (cylinder : cone) will be:
a) 3 : 2
b) 4 : 3
c) 1 : 1
d) 2 : 1
25. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 7 cm and the total height of the toy is 31 cm. Find the volume (in cm³) of the toy. (Take π = 22/7)
a) 4312
b) 4389
c) 4466
d) 4620
26. If a solid cone of volume 64π cm³ is kept inside a hollow cylinder whose radius and height are the same as those of the cone, then the volume of water needed to fill the empty space is:
a) 64π cm³
b) 96π cm³
c) 128π cm³
d) 192π cm³
27. The radii of the base of a cylinder and a cone are in the ratio 2 : 3 and their heights are in the ratio 3 : 4. The ratio of their volumes is:
a) 1 : 2
b) 2 : 3
c) 3 : 4
d) 4 : 3
28. A conical flask is completely filled with water. The radius of its base is 6 cm and its height is 9 cm. The water is poured into a cylindrical flask of base radius 3 cm. The height of water in the cylindrical flask is:
a) 9 cm
b) 12 cm
c) 18 cm
d) 27 cm
29. A cone of height 12 cm and base radius 3.5 cm is carved from a cuboidal block of wood 14 cm × 7 cm × 5 cm. (Take π = 22/7) The percentage of wood wasted in the process is:
a) 40%
b) 50%
c) 60%
d) 70%
30. The radius and height of a cone are each increased by 200%. The percentage increase in the volume of the cone is:
a) 800%
b) 1700%
c) 2600%
d) 2700%
31. If both the radius and height of a right circular cone are increased by 100%, its volume will:
a) increase by 300%
b) increase by 500%
c) increase by 700%
d) increase by 800%
32. If the radius and height of a cone are each increased by 200%, then the volume of the cone becomes:
a) 9 times
b) 18 times
c) 27 times
d) 36 times
33. If the height of a cone is increased by 200%, while its radius remains unchanged, then its volume is increased by:
a) 100%
b) 200%
c) 300%
d) 400%
34. The height of a cone is 24 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone is 1/8 of the volume of the original cone, at what height above the base is the section made?
a) 6 cm
b) 8 cm
c) 12 cm
d) 16 cm
35. If the radius of the base of a cone is 5 cm and its curved surface area is 65π cm², then the volume of the cone is:
a) 100π cm³
b) 150π cm³
c) 200π cm³
d) 250π cm³
36. A right circular cone is carved out of a wooden cube of edge 6 cm such that the wastage of wood is minimum. The volume of the cone is:
a) 54 cm³
b) 36 cm³
c) 72 cm³
d) 108 cm³
37. A right triangle with sides 6 cm, 8 cm and 10 cm is rotated about the side of 6 cm to form a cone. The volume of the cone formed is:
a) 96 cm³
b) 128 cm³
c) 64 cm³
d) 192 cm³
38. The volume of the largest right circular cone that can be cut out of a cube of edge 6 cm is:
a) 36π cm³
b) 72 cm³
c) 108 cm³
d) 54 cm³
39. The radius of the base of a right circular cone is 5 cm and its slant height is 13 cm. Then its volume is:
a) 100π cm³
b) 200π cm³
c) 300 cm³
d) 400 cm³
1. The slant height of a conical hill is 10 cm and the area of its base is 154 cm². (Take π = 22/7) The height of the hill is:
a) 6 cm
b) 7 cm
c) 8 cm
d) 9 cm
2. The base of a conical tent is 14 m in diameter and the height of its vertex is 24 m. (Take π = 22/7) The area of the canvas required to put up such a tent (in square metres) is:
a) 550 m²
b) 616 m²
c) 660 m²
d) 704 m²
3. The height and the radius of the base of a right circular cone are 15 cm and 10 cm respectively. A plane parallel to the base cuts the cone at a distance of 6 cm from the base. The radius of the circular cross-section is:
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
4. A semi-circular sheet of metal of diameter 50 cm is bent into an open conical cup. The depth of the cup is:
a) 20 cm
b) 24 cm
c) 25 cm
d) 30 cm
5. The base of a cone and a cylinder have the same radius 5 cm. They also have the same height 12 cm. The ratio of the curved surface area of the cylinder to that of the cone is:
a) 5 : 4
b) 12 : 13
c) 24 : 13
d) 13 : 12
6. There are two cones. The curved surface area of one is three times that of the other. The slant height of the latter is three times that of the former. The ratio of their radii is:
a) 1 : 1
b) 3 : 1
c) 9 : 1
d) 1 : 3
7. The length of canvas, 2 m wide, required to build a conical tent of height 24 m and base radius 7 m is: (Take π = 22/7)
a) 260 m
b) 270 m
c) 275 m
d) 280 m
8. The lateral surface area of a frustum of a right circular cone is to be found. The area of its base is 49π cm², the diameter of the circular upper surface is 6 cm, and the slant height is 5 cm. The lateral surface area of the frustum is:
a) 60π cm²
b) 65π cm²
c) 70π cm²
d) 75π cm²
9. A right circular conical structure stands on a circular base of 28 m diameter and is 21 m high. The total cost of colour washing for its curved surface at Rs. 5 per square metre is: (Take π = 22/7)
a) rs. 4620
b) rs. 5390
c) rs. 6160
d) rs. 6930
1. The height of a conical tank is 24 cm and the diameter of its base is 14 cm. The cost of painting it from outside at the rate of ₹50 per sq. m is: (Take π = 22/7)
a) ₹11.55
b) ₹13.86
c) ₹15.40
d) ₹18.20
2. A solid metallic cone of height 12 cm and radius of base 14 cm is melted to make spherical balls each of 7 cm diameter. How many such balls can be made? (Take π = 22/7)
a) 8
b) 12
c) 16
d) 24
3. The radius of a metallic cylinder is 7 cm and its height is 10 cm. It is melted and moulded into small cones, each of height 5 cm and base radius 2 cm. The number of such cones formed is:
a) 20
b) 24
c) 28
d) 35
4. A metallic cone of radius 21 cm and height 28 cm is melted and recast into metallic spheres of radius 7 cm. The number of spheres formed is:
a) 6
b) 9
c) 12
d) 15
5. The radius of the base of a conical tent is 7 m and its height is 24 m. Find the cost of canvas required to make the tent, if one square metre of canvas costs rs 50. (Take π = 22/7)
a) rs 5000
b) rs 5500
c) rs 6000
d) rs 6500
1. A drop of water is spherical and its diameter is 1/5 cm. A conical glass has a height equal to the diameter of its rim. If 2000 drops of water fill the glass completely, then the height of the glass (in cm) is:
a) 2 cm
b) 3 cm
c) 4 cm
d) 5 cm
2. A cone is cut by a plane parallel to its base at one-third of its height from the top. Find the ratio of the volume of the smaller cone to that of the remaining frustum.
a) 1 : 8
b) 1 : 26
c) 1 : 9
d) 1 : 3
3. A solid cone of height 12 cm and diameter of its base 16 cm is cut out from a wooden solid sphere of radius 8 cm. The percentage of wood wasted is:
a) 60%
b) 66 2/3%
c) 70%
d) 75%