A solid G is enclosed by the sphere x? + y² + z² = 4, the plane z = 1 and the xy- plane. By using the spherical coordinates, the volume of the solid G can be expressed as sec y 27 p² sin odpddo + | || sin odpddo 1 1 p sin pdpdody V where a, b, c and d are constants. Find the values of a, b, c and d. Then 6. evaluate V.
A solid G is enclosed by the sphere x? + y² + z² = 4, the plane z = 1 and the xy- plane. By using the spherical coordinates, the volume of the solid G can be expressed as sec y 27 p² sin odpddo + | || sin odpddo 1 1 p sin pdpdody V where a, b, c and d are constants. Find the values of a, b, c and d. Then 6. evaluate V.
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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Transcribed Image Text:A solid G is enclosed by the sphere x2 + y + z? = 4, the plane z
and the xy- plane. By
using the spherical coordinates, the volume of the solid G can be
expressed as
= 1
а
sec Y
2T
V =
III p sin pdpdðdy + | 1 p² sin ydpdðdy
ρ' sin φάρdθdφ
b Jo
where a, b, c and d are constants. Find the values of a, b, c and d. Then
6.
evaluate V.
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