I have enough pure silver to coat square meter of surface area. I plan to coat a sphere and a cube. Allowing?
for the possibility of all the silver going onto one of the solids, what dimensions should they be if the total volume of the silvered solids is to be a maximum?
hope you have studied multivariables
f(x,r,µ ) = [4/3]π r^3 +x^3 + µ [ 4π r² + 6 x² - 1] , r & x in meters
compute δf / δx = 0 , δf / δr = 0, and δf / δµ = 0 , find x & r and resulting volume , compare with r = 0 & x = 1 / √6 , then with x = 0 & r = 1 / √(4π) …choose the set with max volume
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