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Lecture

# 8.2 Surface Area of Revolution Overview

Department
Mathematics
Course Code
MAT136H1
Professor
all

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8.2 Challenging Integral Applications
Surface Area of Revolution: Overview
Lateral surface area of a cone:   , where is the slant height and   
For rotation about the x-axis, the radius extends vertically, so    . Then from point
 to , then  
 and the
  . Putting into the equation for the surface area of
revolution:  
  . As   : 
 
 
by the definition for rotating the
curve    over 
Using Leibniz notation: 

, or when the function is written as  , then
the surface area is 

For rotation about -axis:  

.
Substituting  
 for the arc length: 