In this worksheet, we will practice identifying cylindrical and spherical coordinates and converting points and equations between Cartesian, cylindrical, and spherical coordinates.

Q1:

Write the given equation in cylindrical and spherical coordinates.

A
,

B
,

C
,

D
,

E
,

Q2:

Convert the point
from Cartesian coordinates to cylindrical and spherical coordinates,
rounding the value of to two decimal places.

A
,

B
,

C
,

D
,

E
,

Q3:

Express the equation in cylindrical and spherical coordinates.

A
,

B
,

C
,

D
,

E
,

Q4:

Let be a point in spherical coordinates with
and , where
lies on the sphere . Since , the line segment from the origin to
can be extended to intersect the cylinder given by in cylindrical coordinates. Find the cylindrical coordinates of that point of intersection.

A

B

C

D

E

Q5:

Convert the point from Cartesian coordinates to cylindrical and spherical coordinates.

A
,

B
,

C
,

D
,

E
,

Q6:

Write the given equation in cylindrical and spherical coordinates.

A
,

B
,

C
,

D
,

E
,

Q7:

Which of the following is NOT a correct description of the sphere of radius in centered at the origin?

A

B

C

D

Q8:

Convert the point from Cartesian coordinates to
cylindrical, , and spherical, ,
coordinates. Round the value of to two decimal places.

A
,

B
,

C
,

D
,

E
,

Q9:

Convert the point from Cartesian coordinates to cylindrical, , and
spherical, , coordinates. Round the value of to two decimal places.

A
,

B
,

C
,

D
,

E
,

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