Categories
Intermediate

The axe head

A tetrahedron with given vertex coordinates. What is its volume?

Categories
Intermediate

The King’s chamber

A pyramid with a square base and sides that are equilateral triangles contains a cube. If the cube is taking maximum space as shown, what is the fraction of its volume to the pyramid’s volume?

Categories
Advanced

The party hat

A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?

Categories
Intermediate

The pyramid perspective

Two congruent pyramids placed at different distances from the observer appear as equilateral triangles in a square frame. If the closest one is at 100 meter, how far is the distant pyramid?

Categories
Advanced

The lazy spider

A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?

Categories
Beginner

The diagonal dilemma

On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?