### 8.5: Surface Areas of Solids

In this subunit, we will combine what we learned earlier in this unit. Though you might expect that calculating the surface area of a solid will be as easy as finding its volume, it actually requires a number of additional steps. You will need to find the curve-length for each of the slices we identified earlier and then add them together.

Read Section 6.4 (pages 327 through 335). In this beautiful presentation of areas of surfaces of revolution, the author again makes use of rigorously-defined infinitesimals, as opposed to limits. Recall that the approaches are equivalent; using an infinitesimal is the same as using a variable and then taking the limit as that variable tends to zero.

Watch this video from 26:10 to 40:35.

Work through each of the three examples on the page. As in any assignment, solve the problem on your own first. Solutions are given beneath each example.