A monument is made from stone blocks of density 3800kg/m^3. The monument is 15.7m high, 64.8m wide at the base, and 3.6m thick from front th back. How much work was required to build the monument? (Hint: find ycm).
ycm = (1/M) * ∫ydm, M = mass total
The Attempt at a Solution
Take a cross section and get a rectangle.
The length will be: (64.8/15.7) * y
The width will be: (3.6/15.7) * y
Thus, dm = density * length * width * dy
M total = density * volume = 6958742.8
ycm = (1/M) * ∫y * density * length * width * dy (from 0 to 15.7)
Okay, so this solution is wrong. It gives the the ycm as 7.85m. But ycm is actually a third of the height (as it is for triangles).
My question is: what is fundamentally wrong with my approach?
I have the solution though. I don't need that.