Use differentials to estimate the maximum error in the volume of a circular cone due to possible error of 0.1m in the measurement of the radius and 0.30m error in the measurement of the height, if the cone has a radius of base r=3m and a height h=6m. V== πr²h. a. b. C. d. e. 2.7mm2 2.2π m² 2.1π m2 1.9 m² 1.8 m²

An outdoor decorative pond in the shape of a hemispherical tank is to be filled with water pumped into the tank through an inlet in its bottom. Suppose that the radius of the tank is R = 10 ft, that water is pumped in at a rate ofT ft/min, and that the tank is initially empty. As the tank fills, it loses water through evaporation. Assume that the rate of evaporation is proportional to the area A of the surface of the water and that the constant of proportionality is k = 0.01. Output: water evaporates at rate proportional to area A of surface ER- Input: water pumped in at rate 7 ft/min (a) hemispherical tank (b) cross-section of tank (a) The rate of change dv of the volume of the water at time t is a net rate. Use this net rate to determine a differential equation for the height h of the water at time t. The volume of the water shown in the figure is V = TRh -Th, dt where R = 10. Express the area of the surface of the water A = Tr2 in terms of h. dh dt (b) Solve the differential…

The tank shown below is full of water. Recall that the density of water is 1000 kg/m³. Suppose that the pump breaks down after 4.7 x 10°J of work have been done. What is the depth (in meters) of the water remaining in the tank? Make sure your answer is accurate to the nearest tenth. + 3 m - 2 m 3 m 8 m meters Depth of water =

Hi I need help answering question 11 and 13. Thank you.