Question

Identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 49

Answer 1

The surface is a cylindrical surface with radius 7 units

Explanation:

The equation is properly written as:

`\rho^(2) (sin^(2) \phi sin^(2) \theta + cos^(2) \phi) = 49`

The above equation takes the form
`y^(2) + z^(2) = r^(2)`

Where
`y^(2) = \rho^(2) sin^(2) \phi sin^(2) \theta`

`y = \rho sin \phi sin \theta`

and
`z^(2) = \rho^(2)cos^(2) \phi`

`z = \rho cos \phi`

`r^(2) = 49`

r = 7 units

The surface is a cylindrical surface with radius 7 units