Solve Volume of Sphere & Cone w/ Cylinder | Urgent

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To solve the volume of a sphere with cylindrical cuts, the equation z = ±√(j² - x² - y²) is used, with a preference for polar coordinates for integration. For the cone with a cylinder, similar integration techniques are applicable, focusing on establishing the correct ranges. The divergence theorem is questioned for its necessity in these calculations, as the primary goal is to derive the main equations for volume without complete solutions. The discussion emphasizes finding integration limits using dx, dy, dz, or polar coordinates. Understanding these concepts is crucial for accurately determining the volumes in question.
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[URGENT]:How to solve this?

Do i need to use any theorem to solve this such as divergence theorem?

the first question need to find the volume of the sphere that a part in up and bottom being cut( z-axis) and the middle is a hole( cylindrical shape )

the second question need to find the volume of a cone with a cylinder.

for both question, the answer is not need completely solve, just need find the main equation for finding the volume.( I mean just find the range for integration by using dx,dy,dz or using polar coordinate )
Equation for finding volume equation using polar coordinate is prefered.
 

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Why would divergence theorem be needed? For the first one, z = +- sqrt(j^2-x^2-y^2). Put this in a polar integral.
 

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