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Magazine Problem 371
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$[T] r=4$$
Problem 372
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} z=r^{2} \cos ^{2} \theta$$
Problem 373
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} r^{2} \cos (2 \theta)+z^{2}+1=0$$
Problem 374
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} r=3 \sin \theta$$
Problem 376
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} r^{2}+z^{2}=5$$
Problem 377
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} r=2 \sec \theta$$
Problem 378
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $$\mathbf {[T]} r=3 \csc \theta$$
Problem 379
For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$z=3$$
Problem 380
For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$x=6$$
Problem 381
For the following exercises, the equation of a surface in rectangular coordinates is given. Find the equation of the surface in cylindrical coordinates. $$x^{2}+y^{2}+z^{2}=9$$
