Question 433234
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Depends.  Is the apex of the cone a point in the plane of the face of the cube opposite the face containing the base of the cone?  Is the base of the cone a circle that is inscribed in one of the faces of the cube (i.e. is it the largest possible circle such that the diameter of the circle is equal to the measure of one of the edges of the cube)?


Presuming all of the above, the volume of a cone is one-third times the area of the base times the height.  With the presumptions given above, the cone has a volume of:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_{cone}\ =\ \frac{\pi (2^2)\,\cdot\,4}{3}]


Meanwhile, the volume of the cube before being drilled out is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_{wholecube}\ =\ 4^3\ =\ 64]


So the volume of the drilled cube:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_{drilled}\ =\ V_{wholecube}\ -\ V_{cone}\ =\ 64-\ \frac{\pi (2^2)\,\cdot\,4}{3}]


You can do your own arithmetic.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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