Can anyone show me the process and how you would solve this problem? Im having a hard time with this question. thank youA grain of silo, in the shape of a right cylinder with a top that is a hemisphere is to have a capacity of 504π ft^3. Find the radius and height that requirs the least amount of material to construct the silo
Volume of the silo with h height (except the hemisphere) and r radius should equal 504π. π*r^2*h+2/3π*r^3=504π So, h=504/r^2-2/3r. The surface are of the silo: 2π*r*h+2*π*r^2 Substitute above h here to get 1080π/r-4π/3*r^2+2*π*r^2 To minimize the surface area of the silo, take the derivative for r and equate to zero. (also cancel π) -1080/r^2-8/3*r+4*r^2=0 Multiply everything by r^2... -1080-8/3*r^3+4*r^4=0 Solve this numerically...
