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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 13.9.3 .
Consider the cylinder with radius \(a\) and height \(h\) defined parametrically by
\begin{equation*}
\vr(s,t) = a\cos(s) \vi + a\sin(s) \vj + t \vk
\end{equation*}
for
\(0 \leq s \leq 2\pi\) and
\(0 \leq t \leq h\text{,}\) as shown in
Figure 13.9.7 .
Figure 13.9.7. A cylinder.
Set up an iterated integral to determine the surface area of this cylinder.
Evaluate the iterated integral.
Recall that one way to think about the surface area of a cylinder is to cut the cylinder horizontally and find the perimeter of the resulting cross sectional circle, then multiply by the height. Calculate the surface area of the given cylinder using this alternate approach, and compare your work in (b).
