A solid sphere and a solid hemisphere have the same total surface area. The the ratio of their volume is

The radius and the height of a cone are each increased by 20%. Then the volume of the cone increases by

• 20%

• 20.5%

• 62%

• 62%

93.

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius  are dropped in the vessel, 25% water is overflowed. The number of balls is:

• 100

• 400

• 200

• 200

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm ) is

• 30

• 90

• 45

• 45

Radius cross section of a solid circular cylindrical rod is 3.2 dm. The rod is melted and 44 equal solid cubes of side 8 cm are formed. The length of the rod is 

• 56 cm

• 7 cm

• 5.6 cm

• 5.6 cm

A right circular conical structure stands on a circular base of 21 m diameter and is 14 m in height. The total cost of colour washing for its curved surface at 6 per sq m is (Take ) 

• 4365

• 4465

• 3465

• 3365

A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed
is

• 19 cm

• 21 cm

• 23 cm

• 25 cm

The radius of a sphere and right circular cylinder is 'r'. Their volumes are equal. The ratio of the height and radius of the cylinder is

• 3 : 1

• 2 : 1

• 3 : 2

• 4 : 3

The base area of a right pyramid is 57 sq units and height is 10 units. Then the volume of the pyramid is:

• 190 c. units

• 380 c. units

• 540 c. units

• 570 c. units

The volume of the largest sphere (in cm³) that can be drawn inside a cube of side 18 cm is