The radius of a wire is decreased to one-third. If volume remains the same, the length will become

A right curcular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m², is

Two steel sheets each of length a₁ and breadth a₂ are used to prepare the surfaces of two right circular cylinder —one having volume v₁ and height a₂ and other having volume v₂ and height a_1. Then,

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is