Answer:
29260 lb.ft
Explanation:
Elemental Volume of the stone is
dV = πr²dh
r varies linearly from 4 at the base (h=0) to 0 at h=10
Using the concept of similar triangles,
(r/4) = (10-h/10)
r = 4 - 0.4h
dV = π(4 - 0.4h)² dh
dV = π (16 - 3.2h + 0.16h²) dh
dweight = ρdV = 70 dV
dweight = 70π (0.16h² - 3.2h + 16) dh
dWork = dweight x distance
dW = 70π (0.16h² - 3.2h + 16)h × dh)
dW = 70π (0.16h³ - 3.2h² + 16h) dh
dW = (70π) ∫¹⁰₀ (0.16h³ - 3.2h² + 16h) dh
W = (70π) [0.04h⁴ - 1.067h³ + 8h²]¹⁰₀
W = 29260 lb.ft
