A cone and cylinder are of the same radius andsame height. Express ratio of their curved surface areas
cylinder 2 pi r h
cone pi r s where s is the slant height
s^2 = r^2 + h^2
so
pi r sqrt(r^2 + h^2)
ratio cylinder over cone
= 2 pi r h/ [ pi r sqrt(r^2 + h^2) ]
= 2 h/sqrt(r^2 + h^2)