Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
Course: Calculus II
Topic: Geometry
Subtopic: Area of Surface of Revolution


In this lesson we will use definite integrals to find the area of the surface of a solid of revolution. If the solid is a regular shape, such as a cylinder, then we have a formula to find its surface area. However, if the curve is spun to generate the solid is irregular, then calculus is needed to find its surface area. The plan will be, as usual, to find the area of a tiny piece of the surface then add the little areas up to get the surface area..


By the end of this topic you should know and be prepared to be tested on:


Define: solid of revolution, surface, surface area

Supplemental Resources (optional)

Video: Arc Length and Surface Area, Selwyn Hollis's Video Calculus (watch 2nd half)

Lesson: Lengths of Curves and Areas of Surfaces of Revolution, Dale Hoffman's Contemporary Calculus (study surface area sections)