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?
A triangle is formed by a circle radius and an external point. It is divided by the shown chord. What’s the proportion of the angles α and β?
An equilateral triangle is folded with its left side at right angles with the base. What fraction of the total triangle is shaded?
An equilateral triangle and three squares. What’s the angle?
A circle and two semicircles are nested as shown. What’s the proportion of their respective radii a : b : c ?
A regular octagon is coloured as shown. What fraction of its area is red?
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?
A square and two rectangles, connected by two circular arcs, form a square. What is the proportion of the orange to the green area?
Two circles of area π and 9π respectively are contained in a parallelogram. What’s its area?
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?