4. Determine how much the oil level in a cylindrical tank will rise with an increase in temperature from 15^circ C to 40^circ C The density of oil at 15^circ C is 900kg/m^3 Tank diameter d=10m oil fills the reservoir at 15^circ C to a height of H=12 m. Thermal expansion coefficient of oil beta _(T)=6,4cdot 10^-41/degree expansion is not taken into account. V_(15)=pi R^2H rho _(t)=(rho _(15))/(1+beta _(T)(t-15))arrow Delta V=beta _(T)VDelta Tarrow Delta V=pi (d^2)/(4)Delta H

To determine how much the oil level in the cylindrical tank will rise with an increase in temperature from to , we can use the formula for thermal expansion: where is the change in volume, is the thermal expansion coefficient, is the initial volume, and is the change in temperature.Given that the diameter of the tank is and the oil fills the reservoir to a height of at , we can calculate the initial volume of the oil: where is the radius of the tank, which is half of the diameter: Substituting the values, we get: Now, we can calculate the change in temperature: Substituting the values into the thermal expansion formula, we get: Finally, we can calculate the change in height by dividing the change in volume by the cross-sectional area of the tank: Therefore, the oil level in the cylindrical tank will rise by approximately 1.21 meters with an increase in temperature from to .