An artist is slicing an ice cube along the 3 diagonals joining 3 vertices, producing a piece of triangular ice pyramid as shown.

The artist then continues this process 3 more times on other diagonals, thereby creating 3 more pyramids, and finishes his artwork with a perfect tetrahedron in the end.

What is the fraction in volume of this tetrahedron compared to the original ice cube?

$\frac16$
$\frac15$
$\frac12$
$\frac13$
$\frac14$

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The pyramid that the artist cuts out is a pyramid with the right triangle base, whose area is half of the cube's face. For a pyramid with square base (cube's face), the volume is $\dfrac{1}{3}$ of the cube's volume, so the volume of this right-triangular pyramid is half of one-third or $\dfrac{1}{6}$ of the cube's volume.

The artist proceeds 3 more times, so there are 4 such pyramids. Hence, the total volume = $4\times(1/6)$ = $\dfrac{4}{6}$ = $\dfrac{2}{3}$ of the cube's volume.

As a result, the volume of the tetrahedron = 1 - $\dfrac{2}{3}$ = $\dfrac{1}{3}$ of the cube's volume.