Cone in Cube

Geometry Level 5

What is the volume of the largest right cone inscribed in an unit cube?


The answer is 0.3400873808.

View wiki
X X by X X , 17, Taiwan

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

X X
Jun 20, 2018

This isn't complete yet.

The base is halfway between diagonally opposite verteices of the unit cube, inscribed inside a hexagon.The height of the cone is half the diagonal.

The answer is 3 16 π \dfrac{\sqrt 3}{16}\pi

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Will it not cross the cube if the base is half between the diagonally opposite vertices? The base should be at a distance √3/(2+√2) away from a vertices along the diagonal. Then the cone shan't go out of the cube. You may check it.

Alapan Das - 2 years, 2 months ago

Log in to reply

No, it won't cross the cube. Everything is packed nicely inside.

Saya Suka - 2 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...