Let S be a circular cylinder of radius 0.2, such that the center of one end is at the origin and the center of the other end is at the point (5, 0, 4).
Let P be the plane containing the base of the cylinder (i.e., the plane through the origin perpendicular to the axis of the cylinder).
In each case, give a parameterization $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$ and specify the range of values your parameters must take on.
(i)the circle in which the cylinder, S, cuts the plane, P.
(ii)the surface of the cylinder S.

Question

Quizplus · Accepted Answer

The Answer is (i)

\begin{array} { l l } z ( heta ) = \frac { - 0.8 \sin heta } { \sqrt { \left. \$ x ^ { \wedge } 2 + z ^ { \wedge } 2 ight] } } \y ( heta ) = 0.2 \cos heta & 0 \leq heta \leq 2 \pi\x ( heta ) = \frac { 1 \sin heta } { \sqrt { \left. \$ x ^ { \wedge } 2 + z ^ { \wedge } 2 ight] } } &\end{array}

(ii)

\begin{array} { l l } x ( heta ) = \frac { - 0.8 \sin heta } { \sqrt { \left. \$ x ^ { \wedge } 2 + z ^ { \wedge } 2 ight] } } + t & \y ( heta ) = 0.2 \cos heta & 0 \leq heta \leq 2 \pi , 0 \leq t \leq 4 . \z ( heta ) = \frac { 1 \sin heta } { \sqrt { \left. \$ x ^ { \wedge } 2 + z ^ { \wedge } 2 ight] } } + t &\end{array}

Let S Be a Circular Cylinder of Radius 0 (x(θ),y(θ),z(θ))( x ( \theta ) , y ( \theta ) , z ( \theta ) )(x(θ),y(θ),z(θ))

Let S Be a Circular Cylinder of Radius 0 $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$