Riley hobson bence · Problem 3.27

Complex numbers and hyperbolic functions

Mathematics — Methods · hyperbolic-functions-surface-of-revolution

Problem

A closed barrel has as its curved surface the surface obtained by rotating about the

x

-axis the part of the curve

y = a[2 - \cosh(x/a)]

lying in the range

-b \leq x \leq b

, where

b < a\cosh^{-1} 2

. Show that the total surface area,

A

, of the barrel is given by

A = \pi a[9a - 8a\exp(-b/a) + a\exp(-2b/a) - 2b].