Can someone please help me with this problem?

Question

A machinist drilled a conical hole into a cube of metal. If the cube has sides of length 5 cm, what is the volume of the cube after the hole is drilled? Would 92.29 cm³ be correct?

Answer 1

a cube with sides = 5 cm will have volume = 5^3 = 125 cm^3

if the volume after the hole is drilled = 92.29 then the volume of the hole = 125-92.29 = 32.71 cm^3

if the hole is cylindrical, it would have volume = 5(pi)(d/2)^2 = 5pi(r)^2 = 32.71 cm^3

r^2 = 32.71/5pi

r = radius = sqr(32.71/5pi) = about 1.443 cm

if the radius of the hole is about 1.443 cm, then you have the right answer for the volume of the hole

if the hole is conical, it's area is 1/3 of the area of a cylindrical hole

volume of a cone shaped hole = (1/3)5pi(r^2) = 32.71

r^2 = 32.71(3)/5pi

r = sqr(98.13)/5pi) = about 2.5 cm

if the problem had a radius of about 2.4999 which means a diameter of nearly 5 cm, then your calculation for the volume is correct, but this seems strange as the hole's diameter is virtually the same as the cube's side