1
Cylindrical and Spherical Coordinates- HW Problems
1. Change from cylindrical coordinates to Cartesian coordinates.
3𝜋
a. (2, , 3)
4
4𝜋
b. (3, , 1)
3
2. Change from spherical coordinates to rectangular (Cartesian)
coordinates.
𝜋 𝜋
a. (2, , )
4 3
3𝜋 2𝜋
b. (3, , )
4 3
3. Change from rectangular coordinates to cylindrical coordinates and
spherical coordinates.
a. (1, −1, √2 )
b. (−√3 , 1, 2√3)
4. Sketch the solid given by:
a. 0 ≤ 𝜃 ≤ 𝜋, 0 ≤ 𝑟 ≤ 3, 0 ≤ 𝑧 ≤ 3.
𝜋
b. 0 ≤ 𝜃 ≤ 2𝜋 , 0 ≤ 𝜙 ≤ , 0 ≤ 𝜌 ≤ 2.
4
Cylindrical and Spherical Coordinates- HW Problems
1. Change from cylindrical coordinates to Cartesian coordinates.
3𝜋
a. (2, , 3)
4
4𝜋
b. (3, , 1)
3
2. Change from spherical coordinates to rectangular (Cartesian)
coordinates.
𝜋 𝜋
a. (2, , )
4 3
3𝜋 2𝜋
b. (3, , )
4 3
3. Change from rectangular coordinates to cylindrical coordinates and
spherical coordinates.
a. (1, −1, √2 )
b. (−√3 , 1, 2√3)
4. Sketch the solid given by:
a. 0 ≤ 𝜃 ≤ 𝜋, 0 ≤ 𝑟 ≤ 3, 0 ≤ 𝑧 ≤ 3.
𝜋
b. 0 ≤ 𝜃 ≤ 2𝜋 , 0 ≤ 𝜙 ≤ , 0 ≤ 𝜌 ≤ 2.
4
