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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 13.9.2 .
In this activity, we seek a parametrization of the sphere of radius
\(R\) centered at the origin, as shown on the left in
Figure 13.9.5 . Notice that this sphere may be obtained by revolving a half-circle contained in the
\(xz\) -plane about the
\(z\) -axis, as shown on the right.
Figure 13.9.5. A sphere obtained by revolving a half-circle.
Begin by writing a parametrization of this half-circle using the parameter \(s\text{:}\)
\begin{equation*}
x(s) = \ldots \ \ \ \ \ \ \ \ \
z(s) = \ldots.
\end{equation*}
Be sure to state the domain of the parameter \(s\text{.}\)
By revolving the points on this half-circle about the
\(z\) -axis, obtain a parametrization
\(\vr(s,t)\) of the points on the sphere of radius
\(R\text{.}\) Be sure to include the domain of both parameters
\(s\) and
\(t\text{.}\) (Hint: What is the radius of the circle obtained when revolving a point on the half-circle around the
\(z\) axis?)
Draw the surface defined by your parameterization with appropriate technology.
