SOLUTION: a machinist drilled a cone-shaped hole into a solid cube of medal, if the cube has sides of length4 centimeters,what is the volume of the metal after the whole is drilled? use 3.14

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Question 433234: a machinist drilled a cone-shaped hole into a solid cube of medal, if the cube has sides of length4 centimeters,what is the volume of the metal after the whole is drilled? use 3.14 for pi,round to the nearest tenth .
Answer by solver91311(24713) (Show Source):
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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:

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

So the volume of the drilled cube:

You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it