{"id":139,"date":"2021-07-30T17:19:55","date_gmt":"2021-07-30T17:19:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/?post_type=chapter&p=139"},"modified":"2022-11-01T04:30:04","modified_gmt":"2022-11-01T04:30:04","slug":"introduction-to-triple-integrals-in-cylindrical-and-spherical-coordinates","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/introduction-to-triple-integrals-in-cylindrical-and-spherical-coordinates\/","title":{"raw":"Introduction to Triple Integrals in Cylindrical and Spherical Coordinates","rendered":"Introduction to Triple Integrals in Cylindrical and Spherical Coordinates"},"content":{"raw":"

Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates.<\/p>\r\nAlso recall the chapter opener, which showed the opera house l\u2019Hemisph\u00e8ric in Valencia, Spain. It has four sections with one of the sections being a theater in a five-story-high sphere (ball) under an oval roof as long as a football field. Inside is an IMAX screen that changes the sphere into a planetarium with a sky full of [latex]9000[\/latex]\u00a0twinkling stars. Using triple integrals in spherical coordinates, we can find the volumes of different geometric shapes like these.","rendered":"

Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates.<\/p>\n

Also recall the chapter opener, which showed the opera house l\u2019Hemisph\u00e8ric in Valencia, Spain. It has four sections with one of the sections being a theater in a five-story-high sphere (ball) under an oval roof as long as a football field. Inside is an IMAX screen that changes the sphere into a planetarium with a sky full of [latex]9000[\/latex]\u00a0twinkling stars. Using triple integrals in spherical coordinates, we can find the volumes of different geometric shapes like these.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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