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Drilling Through A Sphere

Math brain teasers require computations to solve.

 

Puzzle ID:#35205
Fun:*** (2.13)
Difficulty:*** (2.98)
Category:Math
Submitted By:MarcM1098Aca****

 

 

 



I just drilled straight through the center of a solid sphere, resulting in a 6cm long cylindrical hole. What is the volume remaining in the sphere?

Here are some formulas you may find useful:
Volume of sphere = (4/3)Pi(r^3)
Volume of cap = (1/6)Pi(3R^2+h^2)h
Volume of cylinder = Pi(R^2)H

r = radius of sphere
h = height of cap
R = radius of hole (the cap and the cylinder share this radius)
H = height of cylinder (6cm)

The portion of the sphere that was removed can be thought of as a cylinder with a cap at both ends. A cap is flat on one side (touching the cylinder) and spherical on the other side (the original surface of the sphere).

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