| KU Interactive Mathematics |
| Course Info | Office Hours | Exams | LiveMath | TI | Help |  |
KU | Math Dept | Home |
Surface Area
Question: How do we compute the surface area of the solid obtained by revolving |
Yours Truly answers: The knowledge of surface area builds on that of arc length. Indeed, the general formula is given by  It is the skills for differentiation and basic algebra that separate those who can do the problem from those who cannot. Step 1. The Derivative We need to make a quick decision as to how to differentiate the function. This is when Calculus I skills come into play. The Quotient Rule? Perhaps, but do we foresee something messy ahead, especially when we square the derivative? So, what other approaches? This is when algebra skills come into play. As seen below, having a good start in this surface area problem has nothing to do with Calculus II at all! Step 2. Arc Length Component The tail end of the integrand is computed as follows. No Calculus II skills are needed!  Step 3. Integration Now, we do the integration. But, before we perform the actual integration, it is once again basic algebra skills that make or break this problem.  And, what skills are needed to finish this problem in the last two lines? Not Calculus II, not Calculus I, not even Algebra. It is arithmetic skills! |
| Course Info | Office Hours | Exams | LiveMath | TI | Help | |
KU | Math Dept | Home |
| KU Interactive Mathematics |
Disclaimer • Updated September 4, 2008
Email: mitsuma@kutztown.edu
Phone: +1 (610) 462-WPJW
Phone: +1 (610) 462-WPJW