The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull,15.2 m long and 3.66 m in diameter,filled with gasoline with a density of 880 kg/m³ to make it buoyant.If it is totally submerged in seawater with a density of 1025 kg/m³ and neither rising nor sinking,what is the weight of the Trieste craft? A)127 kN B)227 kN C)327 kN D)427 kN E)527 kN

Question

Quizplus · Accepted Answer

The weight of the Trieste can be found by calculating the buoyant force acting on it, which equals the weight of the displaced seawater. The volume of the Trieste is given by the volume of a cylinder, $V = \pi r^2 h$, where $r = 3.66/2$ meters and $h = 15.2$ meters. The buoyant force (and thus the weight of the Trieste) is $F_b = \rho_{water} V g$, where $\rho_{water} = 1025 \, \text{kg/m}^3$ and $g = 9.8 \, \text{m/s}^2$. Calculating this gives a weight close to 227 kN.

The Bathyscaphe Trieste Consists of a Thin-Walled but Very Strong