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## Homework Statement

Parametrize the portion of the sphere given by x

^{2}+ y

^{2}+ z

^{2}= 7 that lies above z = √3. (use cylindrical coordinates)

## Homework Equations

x

^{2}+ y

^{2}= r

^{2}

## The Attempt at a Solution

x = rcosθ

y = rsinθ

z = z

z = √3

x

^{2}+ y

^{2}+ (√3)

^{2}= 7

x

^{2}+ y

^{2}= 4

r

^{2}cos

^{2}θ + r

^{2}sin

^{2}θ = 4

r

^{2}(cos

^{2}+ sin

^{2}θ) = 4

r = 2

Is this the correct way of parametrization?

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