Practice: Coordinate Systems

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

The point

(x, y) = (1, 3)

in polar is

Q2.

basic

d A

in polar coordinates is

Q3.

basic

d V

in spherical coordinates is

Q4.

intermediate

The volume of a sphere of radius

a

via spherical coordinates is

Q5.

intermediate

Cone

z = x^{2} + y^{2}

in spherical is

Q6.

basic

Best coordinate system for a cylinder

x^{2} + y^{2} \leq 1, 0 \leq z \leq 4

Q7.

basic

Convert

(ρ, θ, ϕ) = (2, π /2, π /2)

to rectangular.

Q8.

intermediate

Volume of upper half-ball

x^{2} + y^{2} + z^{2} \leq 1, z \geq 0

via spherical is