Surface Area and Volume

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2mm. The length of the wire is

• 12 m

• 36 m

• 18 m

• 66 m

The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is

• 5 cm

• 10 cm

• 15 cm

• 24 cm

A circus tent is cylindrical to a height of 4m and conical above it. If its diameter is 105m and its slant height is 40m, the total area of canvas required in m² is

• 1760

• 2640

• 3960

• 7920

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by

• 4.5 cm

• 3 cm

• 4 cm

• 2.5 cm

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

• 48 minutes 15 sec

• 51 minutes 12 sec

• 52 minutes 1 sec

• 55 minutes

A cylindrical vessel 32cm high and 18cm as radius of the base is filled with sand. This is emptied on the ground and a conical heap is formed. If the height of the conical heap is 24 cm, the radius of its base is,

• 12 cm

• 24 cm

• 36 cm

• 48 cm

The curved surface area of a cylinder is 264 m² and its volume is 924 m³ . The ratio of its diameter to its height is

• 3 : 7

• 7 : 3

• 6 : 7

• 7 : 6

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

• 12 cm

• 24 cm

• 30 cm

• 36 cm

A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

(a)  

A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises.

(a)