Sphere/Cylinder
1) A copper sphere having a radius of 6cm is melted and then drawn into a cylindrical wire of radius 2mm. Calculate the length of the wire. 90m
2) A solid metallic cylinder of base radius 2 cm and height 9cm is melted to form a sphere. Calculate:
A) the radius of the sphere. 3
B) the surface of the sphere. (π= 3.14). 113.04
3) The diameter of a copper sphere is 6cm. The sphere is melted and is drawn into a long wire of uniform cross-section. If the length of the wire is 36 cm, find its radius. (Use π=3.14). 1cm
4) The diameter of a sphere is 6 cm. It is melted and down into a wire of a diameter 0.2 cm. Find the length of wire. 36m
5) The diameter of the 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 wire is 108 m, find its radius. 0.3cm
6) A hemispherical bowl of radius 3cm is full of water. The water is emptied into a cylindrical can of radius 2cm. Find the depth of water in the can. 4.5cm
7) A cylindrical vessel 60cm in diameter is partially filled with water. A sphere of diameter 36cm is dropped into it and fully submerged in water. Find the increase in the level of water in the vessel. 8.64cm
8) A building is in the form of a cylinder surmounted by hemispherical vaulted dome and contains 880/21 m³ of air. If the internal diameter of the building is equal to its total height above the floor; find the height of the building. 4m
9) From a sphere of radius 10cm, a right circular cylinder of base diameter 12cm is carved out. Calculate the volume of the right circular cylinder correct to 2 decimal places. 1810.29cm³
10) A cylindrical can whose base is horizontal and of radius 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, Calculate:
A) The total surface area of the can in contact with water when the sphere is in it. 383/2, 7/3
B) The depth of water in the can before the sphere was put into can. Take π to be 22/7 and give your answer as proper fractions.
11) 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 8/3cm. Find the diameter and curved surface area of the cylinder. 14, 352/3
12) Spherical marbles of diameter 1.4 cm are dropped into cylindrical beaker containing some water and her fully submerged . The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm. 150
13) A metallic disc, in the shape of a right circular cylinder, is a height 2.5 m.m and base radius 12cm. Metallic disc is melted and made into a sphere. Calculate the radius of the sphere. 3
14) 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 4 cm and its height is 72cm, find the uniform thickness of the cylinder.
15) What is the least number of solid metallic spheres , each of 6cm diameter, that should be melted and recast to form a solid metal cylinder whose height is 45cm and diameter 4cm.
16) A cylinder boiler, 2m high, is 3.5m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.
17) The volume of a sphere and a right circular cylinder are equal and the diameter of the sphere equals the diameter of the base of the cylinder. Determine the height of the cylinder in terms of the diameter of the sphere.
18) A solid is composed of a cylinder with hemispherical ends . If the whole length of the solid is 105cm and the diameter of the hemisphere ends is 36 cm, find the cost of policy the surface of the solid at the rate of 21 paise per sq. cm.
19) A solid metal cylinder of diameter 28cm the height 42 cm is melted down and recast into sphere of diameter 7cm. Calculate the number of spheres that can be made.
20) A sphere of diameter 14cm is dropped into a cylinder of base radius 10.5cm containing water. Calculate the rise in the lvel of the water in the cylinder, if the sphere is completely submerged, and no water flows out.
21) A spherical shell of lead whose external diameters 18 cm, is melted into a right circular cylinder, 8 cm high and 12cm in diameter. Find the inner diameter of the shell. 16.01 cm
22) a sphere has the same volume as a cylinder whose height is equal to the diameter of its cross section. Find the ratio between their radii. ³√3: ³√2
23) A cylindrical tub of radius 16cm contains water to a depth of 30 cm. A spherical iron ball is dropped into a tub and thus the level of water is raised by 9 cm. What is the radius of the ball ? 12cm
24) A cylinder jar of radius 6cm contains oil. Iron spheres each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by 2 cms? 16
25) A sphere of radius 3 cm is dropped into a cylindrical vessel partly filled with the water. The radius of the vessel is 6cm. If the sphere is submerged completely, by how much will the surface of the water be raised. 1 cm
26) A cylindrical tub of radius 12cm contains water to depth of 20cm. A spherical iron ball is dropped into the tub and thus the level of the water is raised by 6.75 cm. What is the radius of the ball. 9cm
27) A vessel is in the form of hemispherical bowl mounted by hollow cylinder. The diameter of the sphere is 14 cm and the total height of The vessel is 13 cm. Find its capacity. 1642.66cm³
Sphere/Cube/Cuboid:
1) A spherical ball of diameter 21 cm is melted and recast into cubes of side 1cm. Find the number of cubes thus formed. 4851
2) What is the ratio of the volume of the cube to that of the sphere which will fit inside of the cube ? 6:π
3) the largest sphere is carved out of a cube of edge 7cm. Find the volume of the sphere. 539/3cm³
4) A piece of butter 3cm by 5cm by 12cm is placed in a hemispherical bowl of diameter 6.5cm. Will the butter overflow when it melts completely? Yes
5) A solid rectangular block of metal 49cm by 44cm by 18cm is melted and formed into a solid sphere. Find the radius of the sphere. 21cm
6) The diameter of a sphere is 8 cm. Find the length of the edge of a cube which has the same surface area of that surface.
7) How many spherical bullets can be made out of a cube of lead whose edge measures 22 cm, each bullet being 2 cm in diameter. 2541
8) How many spherical lead shot each 0.6 cm in diameter can be made from a rectangular solid 9cm x 11 cm x 12 cm. 10500
9) The largest sphere is carved out of a cube of side 7 cm. Find the volume of the sphere. 179.5 cm³
10) The surface area of a cube is equals to the surface area of a sphere. Find the ratio of volume of cube that of the sphere. √π: √6
Sphere/Cone
1) the radius of a sphere and the base radius of a cone are equal, each being 8cm. If the volumes of these two solids are also equal, find the slant height of the cone. 32.98
2) A cone and a hemisphere have equal bases and equal volumes. find the ratio between the height of the cone and the radius of the hemisphere. 2:1
3) The curved surface of a solid cone with base radius 3cm is 300/7cm². Three such cones are melted and recast into a sphere. Find the radius and surface of the sphere. Assume that there is no loss of metal in melting and recasting. 3cm, 792/7cm²
4) An inverted conical vessel of radius 6cm and height 8cm is filled with water. A sphere is lowered into the vessel. find:
A) the radius of the sphere, given that when it touches the sides, the highest point of the sphere is in level with the base of the cone.
B) volume of water that flows out of conical vessel consequent to lowering the sphere in it. 3 113.04
5) A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 12cm and its height is 8cm. Determine the surface area and volume of the toy. (π=3.14). 413.48cm², 753.6cm³
6) A vessel is in the form of an inverted cone. Its height is 11cm and the radius of its top which is open is 2.5cm. It is filled with water upto the rim. When lead shots, each of which is a sphere of radius 0.25 cm and dropped into the vessel, 2/5 of the water flows out. Find the number of lead shots are dropped into the vessel. 440
7) A hollow sphere of internal and external dimension 4cm and 8cm respectively, is melted into a cone of base diameter 8cm. Find the height of the cone. 14
8) The surface area of a solid metallic sphere is 1256cm². It is melted and recast into solid right circular cone of radius 2.5cm and height 8cm. Calculate:
A) the radius of the solid sphere.
B) the number of cones recast. Take π=22/7. 10, 80
9) A sphere has the same curved surface as the curved surface of a cone of height 36cm and base radius 15cm. Find the radius of the sphere. 12.09cm
10) A sphere of radius 8 cm is melted and recast into a right circular cone of a height 32 cm. Find the radius of the base of the cone. 8cm
11) A hollow sphere of internal and external diameter 4cm and 8 cm respectively is melted into a cone of base diameter 8cm. Find the height of the cone. 14cm
12) A vessel is in the form of an inverted cone. its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
13) a buoy is made in the form of hemisphere surmounted by a right circular base coincides exactly with the plane surface of hemisphere. The radius of the base of the cone is 3.5m and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.
14) A cone of height 15cm and diameter 7cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed .
15) A hollow sphere of internal and external diameters is 4cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of cone. 14cm
16) A cone and a hemisphere have equal bases and equal volumes . Find the ratio of their lengths. 2:1
17) A toy is in the form of a cone mounted on hemisphere of radius 3.5cm. The total height of the toys 15.5 cm. Find the total surface area. 214.5 cm²
18) A toys in the form of a cone mounted on a hemisphere. The diameter of the base the cone is 6 cm and its height is 4 cm. Calculate the surface area of the toy(π= 3.14) 103.62cm²
Cone/Sphere/Cylinder
1) A cone, a hemisphere and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. find the ratio of the circular base. Find the ratio of their whole surface. (√2+1):3:4
2) A toys hemispherical base, cylindrical middle portion and conical top. The radius of the hemisphere, cylinder, the base of the cone and heights of all the three portions are equal. If the number of units in the volume of the toy is the same as the number of units on its surface area. Find the total height of the toy. 8.121 cm
Cylinder/Sphere/Cone
1) Find the ratio of the volumes of a cylinder, a cone and sphere, if each has the same radius and the same height. 3:1:2
2) A cone, a hemisphere and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. Find the ratio of their whole surfaces. (√2+1):3:4
3) A solid consisting of right circular cone, standing on a hemisphere is placed upright in a right circular cylinder full of water and touched the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6cm, the radius of the hemisphere is 2 cm and the height of the cone is 4cm. Give your answer to the nearest cubic centimetre. (π=22/7). 2860/21
Diagrammatic Questions:
1) With reference to the figure given alongside,
a) The total area of the internal surface, excluding the base. 231m²
b) The internal volume of the container in m³. 1078/3 m3
2) The figure shows the cross-section of an ice cream cone consisting of a cone surmounted by a hemisphere.
a) the volume of the ice-cream in the cone( the unshaded portion including the hemisphere) in cm³.
b) the volume of the outer shell (the portion) in cm³.
give your answer correct to the nearest cm³. 175cm³, 50cm³
3) In the given figure , a cylinder is surmounted by a cone at one end and a hemisphere at the other end,
4) A solid wooden toy is in the shape of a right circular cone mountained 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 wooden toy . Also, find its surface area. 96.36cm²
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