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Problem 42 Easy Difficulty
The solid upper hemisphere of the sphere of radius 2 centered at the origin
Answer
$x^{2}+y^{2}+z^{2} \leq 4$ where $z \geq 0$
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Video Transcript
Yeah, let's write mathematical statements that define the region of the upper hemisphere of the solid sphere centered at the origin with radius too. So the silence here, Senator, the origin with radius too. It's gonna be a sphere right here. The boundary of that sphere. It's gonna have the equation X square plus why square plus the square equals two square. But we don't just want the edge of this year. We want this solid sphere. Yes, we want that and all the points on the inside X Where? Let's slice where, plus the square, less than or equal 24 But we only want the upper half. So you want to cut it off right here along this circle and not include the bottom half? Well, that's an extra restriction just on Z. We're forcing Z to be non negative and so we still want all the points inside the sphere with the added a requirement that Z can't be negatives and that will give us region that we want
Rose-Hulman Institute of Technology
Topics
Vectors
Top Calculus 3 Educators
Heather Z.
Oregon State University
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
Samuel H.
University of Nottingham