   Chapter 16.6, Problem 5E

Chapter
Section
Textbook Problem

Identify the surface with the given vector equation.5. r(s, t) = ⟨s cos t, s sin t, s⟩

To determine

To identify: The surface with the vector equation r(s,t)=scost,ssint,s .

Explanation

Given data:

The vector equation is given as follows.

r(s,t)=scost,ssint,s

Formula used:

Write the expression for a circular cone that symmetric to the z-axis.

z2=x2+y2 (1)

Write the vector equation as follows.

r(s,t)=scost,ssint,s

Write the parametric equations from the vector equation as follows.

x=scost,y=ssint,z=s

Take square on both sides of the symmetric expression x=scost .

x2=(scost)2=s2sin2t

Take square on both sides of the symmetric expression y=ssint .

y2=(ssint)2=s2sin2t

Add the expressions x2 and y2 as follows

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