Use differentials to estimate the amount of material in a closed cylindrical can that is 60 cm high and 24 cm in diameter if the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick. Remember we are estimating the amount of material here, not trying to find an exact representation of the amount of material used. How can a differential of the volume of a cylinder help with this? The differential for the volume is

A pyramid of height 500 ft has a square base 700 ft by 700 ft. Find the area A at height h. A(h) =          If the rock used to build the pyramid has a weight-density of approximately  w = 100 lb/ft3,  how much work (in ft-lb) did it take to lift all the rock?       Assume there were 10,000 workers each working 10 hours a day, 5 days a week, 50 weeks a year. If the workers, on average, lifted ten 100 lb rocks 2 ft/hr, how long (in months) did it take to build the pyramid

Use linearization to estimate the change in volume of a sphere when its radius changes from r to r+ Δr. Then calculates the exact value of the volume change and calculates the difference of both results

H.W. 1) Calculate the volume of cylinder has 15 m height and 8 m diameter. 2) If we have other cylinder with the same height but it volume greater than first cylinder by 20%, how long its radius? 3) Write a program to calculate the volumetric and mass flow rate of a liquid flowing in a pipe with a velocity equal to 0.5 m/s. Knowing that the diameter of this pipe is 0.1 m and the density of this liquid is 890 kg/m³ ? 4) For the following distillation column write a code to find the value of stream B and the compositions of stream D? D=80 X% ? S%? T%? Z% ? F=100kg 15% X 25% S 40% T 20% Z B=? 15% X 25% S 40% T 20% Z 9 5) Compute the reaction rate constant for a first-order reaction given by the -E/RT Arrhenius law k = A e at a temperature T = 500 K. Here the activation energy is E=20 kcal/mol and the pre-exponential factor is A=10¹3 s¹. The ideal gas constant is R=1.987 cal/mol K.