Final answer:
To find the mass of the liquid in the vat, we need to know the volume of the cylindrical vat and the density of the liquid, which is not provided in the question. The pressure at the bottom of the vat can help us find the density if we know what the liquid is, but since we don't have this information, we cannot calculate the mass of the liquid.
Step-by-step explanation:
The student has asked for the mass of the liquid in a cylindrical vat given the pressure at the bottom, the diameter of the vat, and the depth of the liquid. To find the mass of the liquid, we first need to calculate the volume of the liquid and then use the density to calculate the mass.
Let's calculate the volume of the liquid using the formula for the volume of a cylinder V = πr^2h, where r is the radius and h is the height (depth) of the cylinder. The diameter is given as 0.4 m, so the radius r is half of that, which is 0.2 m. The height h is given as 3 m. So the volume V = π * (0.2 m)^2 * 3 m.
Now we know that the pressure at the bottom of the vat is 1.7 atm. To convert atmospheric pressure to Pascals, we use the conversion 1 atm = 101325 Pa. So the pressure P = 1.7 atm * 101325 Pa/atm.
Knowing the pressure at the bottom of the vat allows us to use the formula P = h ρg, where h is the height of the liquid, ρ (rho) is the density, and g is the acceleration due to gravity (9.8 m/s^2). We can rearrange this formula to solve for the density ρ = P / (hg). Once we have the density, we can then find the mass by multiplying the density by the volume of the liquid, m = ρ * V.
However, since the density is not given directly in the problem, we will need an additional piece of information such as the type of liquid or its density under these conditions to determine the mass precisely. In this example, the density of the liquid is missing, which is crucial for calculating the mass. Therefore, we cannot provide the mass of the liquid without this piece of information.