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14. a. Hemisphere cut by cylinder Find the area of the surface cut from the hemisphere x? + y² + z² = 4, z > 0, by the cylinder x + y² = 2x. b. Find the area of the portion of the cylinder that lies inside the hemisphere. (Hint: Project onto the xz-plane. Or evaluate the integral Jh ds, where h is the altitude of the cylinder and ds is the element of arc length on the circle x? + y² = 2x in the xy-plane.) Hemisphere z = V4 – r2 Cylinder r = 2 cos 0

14. a. Hemisphere cut by cylinder Find the area of the surface cut from the hemisphere x? + y² + z² = 4, z > 0, by the cylinder x + y² = 2x. b. Find the area of the portion of the cylinder that lies inside the hemisphere. (Hint: Project onto the xz-plane. Or evaluate the integral Jh ds, where h is the altitude of the cylinder and ds is the element of arc length on the circle x? + y² = 2x in the xy-plane.) Hemisphere z = V4 – r2 Cylinder r = 2 cos 0

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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14. a. Hemisphere cut by cylinder Find the area of the surface cut from the hemisphere x? + y² + z² = 4, z > 0, by the cylinder x + y² = 2x. b. Find the area of the portion of the cylinder that lies inside the hemisphere. (Hint: Project onto the xz-plane. Or evaluate the integral Jh ds, where h is the altitude of the cylinder and ds is the element of arc length on the circle x? + y² = 2x in the xy-plane.) Hemisphere z = V4 – r2 Cylinder r = 2 cos 0
Transcribed Image Text:14. a. Hemisphere cut by cylinder Find the area of the surface cut from the hemisphere x? + y² + z² = 4, z > 0, by the cylinder x + y² = 2x. b. Find the area of the portion of the cylinder that lies inside the hemisphere. (Hint: Project onto the xz-plane. Or evaluate the integral Jh ds, where h is the altitude of the cylinder and ds is the element of arc length on the circle x? + y² = 2x in the xy-plane.) Hemisphere z = V4 – r2 Cylinder r = 2 cos 0
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