A pillar 2m tall stands on a square base, 20cm on a side. The peculiar thing about this pillar is that its top, which is parallel to the base, is an equilateral triangle 16cm on a side.
The four edges running the length of the pillar are linear. Two of these edges meet at one corner of the triangle, and the edge of the triangle opposite this vertex is parallel to two edges of the square. All horizontal cross sections have straight edges.
If the pillar is made of basalt (density = 2.8 g/cm^3), what is its total mass?
My answer is: 236.957 Kg.
The horizontal cross-section varies between a square at the bottom and an equilateral triangle at the top. Typically this is a trapezium with parallel sides length 20-x/50 and 20-x/10 and the perpendicular distance between them is 20 - x(1/10-sqrt(3)/25), where x is the height of the cross-section above the base in cm. The area of a trapezium is the average of the 2 parallel sides multiplied by the perpendicular separation. Integrating this area over the range corresponding to the pillar's height gives the pillar's volume, 84627.69 cc, and hence the mass.
My solution
