# Worksheet: Cylindrical and Spherical Coordinates

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,