Hello! I was wondering how we are supposed to get to the boundaries of the angle when replacing x and y with the polar coordinates rcos and rsin... For r I understand that the boundaries will be from 0 to a, since x2+y2<=a2, so r2<=a2, and hence r<=a, but how do we get to the boundaries of the angle needed to evaluate the integral? 33. Average height of a hemisphere Find the average height ofVa²-x² - y² above the diskthe hemispherical surface z = Va²x² + y² ≤ a² in the xy-plane.

Answered: Image /qna-images/answer/fcfa3870-2760-4355-b050-05b1acc15fd0.jpg

Answered: 33. Average height of a hemisphere Find…

33. Average height of a hemisphere Find the average height of y² above the disk the hemispherical surface z = Va² - x² + y² ≤ a² in the xy-plane.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Question

Hello! I was wondering how we are supposed to get to the boundaries of the angle when replacing x and y with the polar coordinates rcos and rsin... For r I understand that the boundaries will be from 0 to a, since x²+y²<=a², so r²<=a², and hence r<=a, but how do we get to the boundaries of the angle needed to evaluate the integral?