A solid metal cuboid with dimensions 11 cm, 18 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of spheres formed is :

1. 378

2. 1134

3. 1512

4. none of these

By applying force on an uniform metallic wire, the wire is extended four times along its length with same width all around. Then :

(i) The volume of metal in both the cases is same.

(ii) The surface area of solid wires in both the cases is same.

Which of the above statements is/are true?

1. only (i)

2. only (ii)

3. both (i) and (ii)

4. neither (i) nor (ii)

A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
(Answer correct to the nearest integer)

A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.