Sphere Volume Above Paraboloid (Corrected)

Calculus Level 3

Consider a sphere and a paraboloid:

x 2 + y 2 + z 2 = 1 z = ( x − 1 3 ) 2 + ( y − 1 2 ) 2 − 1 2 \large{x^2 + y^2 + z^2 = 1 \\ z = \left(x - \frac{1}{3} \right)^2 + \left(y - \frac{1}{2} \right)^2 - \frac{1}{2}}

What is the volume of the portion of the sphere which lies above the paraboloid (meaning greater z z )?

Note: There was an error in the first posting of this problem, which I have since corrected


The answer is 1.6442.

Steven Chase by Steven Chase , 37, USA

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