Subject: Mathematics Class: 10th Page no-
1. If the number on the surface of a sphere is equal to the number of cubic centimeter in its volume. What is the diameter of the sphere.
2. A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
3. A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. Find the volume and the total surface area of the toy.
4. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm. Find the volume of the toy.
5. Right circular cylinder having 12 cm and height 15 cm is full of ice-cream. The ice cream is to be filled in cones of height 12 cm and diameter 6 cm having hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
6. A vessel in the form of hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 14 cm and the total height of the vessel is 13 cm. Find its capacity.
7. Building is the form of a cylinder surmounted by a hemispherical valuated done and contains of air. If the internal diameter of the building is equal to its total height above the floor. Find the height of the building.
8. A solid sphere of radius 6 cm is melted into a hallow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm. Find the thickness of the cylinder.
9. A hemispherical bowl of internal radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottle needed to fill the whole water of the bowl.
10. A cylinder of radius 12 cm contain water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.
11. Marbles of diameter 1.4 m are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that water level rises by 5.6 cm.
12. A sphere of diameter 6 cm is dropped in a right circular cylinder vessel partly filled with water. The diameter of cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much level of water rise in the vessel.
13. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and surface area of the solid.
14. A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub.
15. The diameter of the internal and external surface of a hallow hemispherical shell are 6 cm ad 10 cm. If it is melted and recast into a solid cylinder of diameter 14 cm. Find the height of cylinder.
16. The internal and external diameter of a hallow hemispherical vessel are 24 cm and 25 cm. If the cost of painting of the surface area is Re. 5.25. Find the total cost of painting the vessel all over.
17. The diameter of copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross section. If the length of the wire is 108 m. Find its diameter.
18. A cylindrical container is filled with ice cream, whose radius is 6 cm and height is 15 cm. The whole ice cream is distributed among 10 children in equal cones having hemispherical tops. If the height of the conical portion is 4 times the radius of its base. Find the radius of the ice cream cone.
19. A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the others. The radius and height of cylindrical parts are 5 cm and 13 cm. The radius of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.
20. The diameter of the internal and external surfaces of a hallow spherical shell are 6 cm and 10 cm. If it is melted and recast into a solid cylinder of height cm. Find the diameter of the cylinder.
21. The surface area of sphere and cube are equal prove that their volumes are in the ration of .
22. The water for a house is stored in a hemispherical tank. Whose internal diameter is 14 m when it contains 50 kiloliter of water, the tank is refilled to its capacity the volume calculate the volume of water pumped in for refilling.
23. A vessel in the shape of a cuboids contains some water. If three identical spheres are immersed in water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160and its height is 12 cm. Determine the radius of any of the sphere.
1. The total surface of a sphere is 3850 . Find the diameter of the sphere.
2. The surface area of sphere is 154 . Find its volume.
3. The trunk of a tree is cylindrical and its circumference is 176 cm. If the length.
4. The curved surface area of a cylindrical pillar is 264 and its volume is 924 . Find the diameter and the height of the pillar.
5. The difference between inside and outside of a cylindrical tube 14 cm long is 88 . If the volume of the tube is 176 . Find the inner and outer radius of the tube.
6. A cylindrical tube at both ends is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm calculate the volume of the metal.
7. A rectangle sheet of paper can be transformed into curved surface of a right circular cylinder in two ways either by rolling the paper along its length or by rolling along its breadth. Find the ratio of the volumes of the two cylinder so formed.
8. Find the length of 13.5 kg of copper wire of diameter 4 mm when 1 of copper weights 8.4 gm.
9. A cylindrical vessel with out lid has to be tin coated on its both sides if the radius of the base is 70 cm and its height is 1.4 m. Calculate the cost of tin coating at the rate of Rs. 3.50 per 1000 .
10. In the middle of a rectangular field measuring a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of field is raised.
11. If 1 cm³ of gold weights 21 gm. Find the weight of the gold pipe of length 1 m with a bore of 3 cm in which the thickness of the metal pipe is 1 cm.
12. A well is 6 m deep and the cost of cementing its inner surface at 50 paise per is Rs. 1320. Determine the diameter of the well.
13. The radius and height of cone are in the ratio 3 : 4 and its volume is 301.44 cm³. What is its radius what is the slant height
14. The inner of a building is in the form of cylinder of diameter 4.3 m and height 3.8 m surrounded by a cone whose vertical angles is a right angle. Find the area of the surface and the volume of the building
15. A conical tent is to accommodate 11 persons. Each person must have 4 m² of space on the ground and 20 m³ of air to breadth. Find the height of the cone.
16. Water flows at the rate of 10 meter per minute through a cylindrical pipe 5 m. m. in diameter. How long would it take to fill a conical vessel whose diameter of base is 40 cm and depth 24 cm.
17. Two cones have their heights in the ratio 1 : 3 and the radius of their bases in the ratio 3 : 1. Find the ratio of their volumes.
18. A conical tent has the area of its base is 154 m² and that of the curved surface is 550 m². Find the volume of tent.
19. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is of the volume of the given cone, at what height above the base the section has been made.
20. Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if a rain fall of 1 cm has fallen.
21. If the radius of the circular ends of a conical bucket is 45 cm high are 28 cm and 7 cm. Find the capacity of the bucket.
22. The perimeter of the ends of the frustum of a cone are 96 cm and 68 cm. If the height of the frustum be 20 cm. Find its radius , slant height, volume and total surface area.
23. An oil funnel of tin sheet of a cylindrical portion 8 cm long attached to a frustum of a cone. If the total height be 16 cm the diameter of the cylindrical portion 1 cm and diameter of the top of the funnel 10 cm. Find the area of tin required.
24. A hallow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface to the remainder is of the curved surface of the whole cone. Find the ratio of the line segment into which the cones altitudes is divided by the plane.
25. A cylinder of radius 12 cm contains water to a depth off 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.