concrete piles and centroids.

**7) **

**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?