A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, then the thickness of gold [given ] is approximately.

• 5.038 m

• 5.190 cm

• 1.038 cm

• 0.518 cm

A circular swimming pool is surrounded by a concrete wall 4m wide. If the area of the concrete wall surrounding the pool is  that of the pool, then the radius (in m) of the pool is

• 20

• 30

• 16

• 8

A cone, a cylinder and a hemisphere stand on equal bases and have equal heights. The ratio of their volumes is

• 2 : 3 : 1

• 2 : 1 : 3

• 1 : 3 : 2

• 1 : 2  :3

A conical cup is filled with ice cream. The ice-cream forms a hemispherical shape on its open top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice-cream is 

• 1078 cubic cm

• 1708 cubic cm

• 7108 cubic cm

• 7180 cubic cm

A.

1078 cubic cm

Volume of the ice-cream = Volume of hemisphere part + Volume of conical part.
Radius (r) = 7 cm.
Volume of hemisphere = 

Volume of conical part = 
            

∴  Volume of ice-cream

A conical iron piece having diameter 28 cm and height 30cm is totally immersed into the water of a cylindrical vessel, resulting in the rise of water level by 6.4 cm. The diameter (in cm) of the vessel is

• 3.5 

• 

• 35

• 32