# Calculus

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Bruce has commissioned the construction of an open-top rectangular tank to be fashioned from a 3m by 5m sheet of steel. Squares will be cut from each corner and sides will be bent upward to form the tank to be used for live bait storage. Find the dimensions of the squares that need to be cut from each corner of the steel sheet in order to provide the maximum volume for the tank.

• Calculus -

the base will be (3-2x) by (5-2x) if a square of side x is cut from each corner.

v = x(3-2x)(5-2x) = 4x^3-16x^2+15
dv/dx = 12x^2-32x+15
dv/dx=0 when x = 1/6 (8-√19) = .6068, or 60.7 cm

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