Question

a cylindrical column has height 30ft and circumference 8ft. A garland is wound evenly 5 times around the column, reaching tol to bottom. show that the garland must be at least 50ft long

Answer 1

let length of  garland is k ft .

since garland wound evenly 5 times around the column so, total area covered by  wounding = 5k ft².....(1)

now,

garland is wounded around curved area of cylindrical column along circumference.

now,

curved area of cylindrical column = circumference x height = 30 ft x 8 ft = 240 ft² .....(2)

since garland is not perfectly wounded because all 5 parts are connected so required length is more than curved area so,

from 1 and 2

5k 240

k 48 ft   

(hence proved)