In this worksheet, we will practice using cylindrical and spherical coordinates to study of three-dimensional phenomena for some models.

**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 ,