Perform the same computation as in Prob. 5.22, but for the frustrum of a cone as depicted in Fig. P5.23. Employ the following values for your computation: r₁ = 0.5 m, r₂ = 1 m, h = 1 m, ρ_f = frustrum density = 200 kg/m³, and ρ_w = water density = 1,000 kg/m³.

 

Data From Problem 5.22

According to Archimedes’ principle, the buoyancy force  is equal to the weight of fluid displaced by the submerged  portion of the object. For the sphere depicted in Fig. P5.22, use bisection to determine the height, h, of the portion that is above water. Employ the following values for your computation: r = 1 m, ρ_s = density of sphere = 200 kg/m³, and ρ_w = density of water = 1,000 kg/m³. Note that the volume of the above-water portion of the sphere can be computed with 

V 3* (ri + r + rr2)