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(a) Use cylindrical coordinates to evaluate the integral 6 √36-y² f (x² + y²)³/2dzdxdy. Sketch the 36-y -6 region of integration.

(a) Use cylindrical coordinates to evaluate the integral 6 √36-y² f (x² + y²)³/2dzdxdy. Sketch the 36-y -6 region of integration.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 2 (a) Use cylindrical coordinates to evaluate the integral 36-y √36-(x² + y²3¹/2dzdxdy. Sketch the 36 -6 region of integration. (b) A cake is shaped like a hemisphere of radius 4 with base on the xy-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the xy-plane and separated by an angle of . (b1) Use a double integral to find the volume of the slice for (b2) Now suppose that the cake is shaped like a cylinder with the same radius and you take a slice in the same way with the same angle. How high the cake should be so that you get the same amount of cake as in part (bl)?
Transcribed Image Text:Question 2 (a) Use cylindrical coordinates to evaluate the integral 36-y √36-(x² + y²3¹/2dzdxdy. Sketch the 36 -6 region of integration. (b) A cake is shaped like a hemisphere of radius 4 with base on the xy-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the xy-plane and separated by an angle of . (b1) Use a double integral to find the volume of the slice for (b2) Now suppose that the cake is shaped like a cylinder with the same radius and you take a slice in the same way with the same angle. How high the cake should be so that you get the same amount of cake as in part (bl)?
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