Question

Find a parametric representation for the surface.

the part of the sphere
x²+y²+z²=144
that lies between the planes z= -6 and z= 6.
(Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of θ and/or ϕ.)

Answer 1

To find the parametric representation for the surface between the planes z = -6 and z = 6 on the sphere x² + y² + z² = 144, we can use spherical coordinates. The parametric representation is x = 12*sin(θ)*cos(ϕ), y = 12*sin(θ)*sin(ϕ), z = 12*cos(θ).

Step-by-step explanation:

To find a parametric representation for the surface between the planes z = -6 and z = 6 on the sphere x² + y² + z² = 144, we can use spherical coordinates. Spherical coordinates are represented by the equations:

x = r*sin(θ)*cos(ϕ)

y = r*sin(θ)*sin(ϕ)

z = r*cos(θ)

Restricting the values of θ and ϕ to the range between -π/2 and π/2, we can define the parametric representation for the surface as:

x = 12*sin(θ)*cos(ϕ)

y = 12*sin(θ)*sin(ϕ)

z = 12*cos(θ)