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(b) A cake is shaped like a hemisphere of radius 2 with base on the ry-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the zy-plane and separated by an angle of ø. (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)?

(b) A cake is shaped like a hemisphere of radius 2 with base on the ry-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the zy-plane and separated by an angle of ø. (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)?

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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(b) A cake is shaped like a hemisphere of radius 2 with base on the ry-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the ry-plane and separated by an angle of þ. (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:(b) A cake is shaped like a hemisphere of radius 2 with base on the ry-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the ry-plane and separated by an angle of þ. (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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