Search results for "Find the surface area of the portion of the sphere x^2+y^2+z^2=4 that is above xy-plane and within the cylinder x^2+y^2=1  use polar coordinates to evaluate the integral

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to parametrize the given surface in spherical coordinates, such that:

`x = r*sin theta*cos phi`

`y = r*sin theta*sin phi`

`z = r*cos theta `

`r = sqrt(x^2 + y^2 + z^2)`

The problem provides the information that `x^2 + y^2 + z^2 = 4` ,such that:

`r = sqrt(4) => r = 2`

`x = 2*sin theta*cos phi, y = 2*sin theta*sin phi, z = 2*cos theta `

You need to evaluate the integral, such that:

`int int_S f(x,y,z) dS = int_0^(pi/6) int_0^(2pi) 16(sin theta sin phi)^2 sin theta d theta d phi`

`int int_S f(x,y,z) dS = pi(32 - 18sqrt3)/3`

Hence, evaluating the surface area of the portion of the sphere, yields` int int_S f(x,y,z) dS = pi(32 - 18sqrt3)/3.`

redths69's profile pic

redths69 | eNotes Newbie

Posted on

You need to parametrize the given surface in spherical coordinates, such that:

The problem provides the information that ,such that:

You need to evaluate the integral, such that:

Hence, evaluating the surface area of the portion of the sphere, yields

This is not what I asked for I wanted done in polar 

 

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