There is a wooden sphere of radius  The surface area of the largest possible cube cut out from the sphere will be

• 864 cm²

• 

• 462 cm²

• 462 cm²

A hollow cylindrical tube 20 cm long is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume (in cubic cm.) of iron used in making the tube is 

• 1760

• 440

• 220

• 220

If the radius of a right circular cylinder open at both the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface area of the cylinder thus formed

• remains unaltered

• is increased by 25%

• is increased by 6.25%

• is increased by 6.25%

A cylindrical pencil of diameter 1.2 cm has one of its ends sharpened into a conical shape of height 1.4 cm. The volume of the material removed is

• 1.056 cm³

• 4.224 cm³

• 10.56 cm³

• 10.56 cm³

A solid cylinder has the total surface area 231 square cm. If its curved surface area is  of the total surface area then the volume of the cylinder is

• 154 cu. cm.

• 308 cu. cm.

• 269.5 cu. cm.

• 269.5 cu. cm.

The lateral surface area of frustrum of a right circular cone. If the area of its base is  and the diameter of circular upper surface area is 4 cm and slant height is 6 cm, will be

87.

A hemispherical bowl of internal radius 9 cm, contains a liquid. This liquid is to be filled into small cylindrical bottles of diameter 3 cm and height 4 cm. Then the number of bottles necessary to empty the bowl is

• 18

• 45

• 27

• 27

The diameter of a sphere is twice the diameter of another sphere. The surface area of the first sphere is equal to the volume of the second sphere. The magnitude of the radius of the first sphere is

• 12

• 24

• 16

• 16

The amount of concrete required to build a concrete cylindrical pillar whose base has a perimeter 8.8 metre and curved surface area 17.6 square metre, is 

• 8.325 m³

• 9.725 m³

• 10.5 m³

• 10.5 m³

A right circular cylinder having diameter 21 cm and height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The number of such cones to be filled with ice cream is

• 54

• 44

• 36

• 36