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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.8.8 .
(a) Convert
\((x,y,z)=(1,2,3)\) to cylindrical coordinates.
(b) Use inequalities on cylindrical coordinates to describe the region given by the 6th octant.
(c) Convert the cone
\(z^2=x^2+y^2\) to cylindrical coordinates. Write a couple of sentences to make sense of how you can simplify your conversion and describe the shape of the graph in terms of
\(z\) and
\(r\text{.}\)
(d) Draw a plot of the surface in
\(\R^3\) with equation
\(r=2\) in cylindrical coordinates. Write a couple of sentences about the shape and properties of this surface.
(e) Draw a plot of the region given by
\(0 \leq \theta \leq \pi, 0 \leq r \leq 2, 0 \leq z \leq r^2 \text{.}\) Write a couple of sentences about the shape and properties of this region.
