A solid E is bounded by the sphere z = -x² - y² on the top and the xy-plane (z = 0). The projection of the solid into xy - plane is the half-disk shown below. Write a triple integral that will calculate the volume of the solid. Write the final integral in terms of x, y, z but do not evaluate the integrals. x²+ y² = 64 -5 -5 X

Algebra: Structure And Method, Book 1
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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
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A solid E is bounded by the sphere z = -x² - y² on the top and the xy - plane
(z = 0). The projection of the solid into xy - plane is the half-disk shown below. Write a triple
integral that will calculate the volume of the solid. Write the final integral in terms of x, y, z but do
not evaluate the integrals.
x² + y² = 64
-5
5
-5
5
X
Transcribed Image Text:A solid E is bounded by the sphere z = -x² - y² on the top and the xy - plane (z = 0). The projection of the solid into xy - plane is the half-disk shown below. Write a triple integral that will calculate the volume of the solid. Write the final integral in terms of x, y, z but do not evaluate the integrals. x² + y² = 64 -5 5 -5 5 X
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