Solve Volume of Sphere & Cone w/ Cylinder | Urgent

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SUMMARY

This discussion focuses on calculating the volumes of a sphere with a cylindrical hole and a cone with a cylinder. The primary method suggested involves using polar coordinates for integration. The equation for the sphere's volume is defined by the limits z = ±√(j² - x² - y²), which is to be integrated in polar coordinates. The divergence theorem is questioned for its necessity in these calculations, indicating a preference for direct volume equations.

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  • Understanding of polar coordinates in calculus
  • Knowledge of volume integration techniques
  • Familiarity with the divergence theorem
  • Basic geometry of spheres, cones, and cylinders
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yongkiat
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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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