Question

19. Minimizing surface area. Mendoza Soup Company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 32 ft. What dimensions will minimize surface area? What is the minimum surface area?

Answer 1

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Solution Volume = 32 ft² open Volume x²y -So Surface me = x + tuxy given Volume = 32 ft² xy - 32 y = 32 x² S = x² + 4x (322) x² + 128 х ds 2x 128 dx 22 ds da

2x - 128 x² X 128 2 x² - 64 2=4 32 32 11 ya = 2 x2 16 So dimension x= 4 ft of rectangular metal tank is (base length width) (height) y = 2 ft