Pile foundations are the part of a structure used to carry and transfer the load of the structure to the bearing ground located at some depth below ground surface.
A concrete pile for a domestic dwelling has a radius of 1000 mm at its base, and 2000 mm at the top. It is 2000 mm deep and the sides slope uniformly.
Find the volume of concrete needed to form this pile.
A plinth is formed in the shape of a hemispherical dome, radius 4 m, with its top 1 m removed. Using integration, find the position of the plinth’s centroid along its axis of symmetry.
i think i just need volume of a frustrum for first part,with base radius 2000 and top radius 1000 and height 2000??
how do i go about the second part?
im thinking of taking y=x^2 and rotating about y-axis then doing the y bar = integral yx^2/integral x^2 with limits x=0 to 4. been a while since doing this but i think that would give me y bar for the dome. is it as simple as just doing the limits from 0 to 3 to do the dome with 1m cut off?