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27 July, 20:17

Find the dimensions of a closed right circular cylindrical can of smallest surface area whose volume is 128pi cm^3

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  1. 27 July, 23:00
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    The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to π r2h.

    V = π r2h = 128 pi

    r2h = 128

    h = 128/r2

    A = 2πr2 + 2πrh

    A = 2πr2 + 2πr * (128/r2)

    A = 2πr2 + 256 π / r

    the optimum dimensions is determined by taking the first derivative and equating to zero.

    dA = 4 πr - 256 π / r2 = 0

    r = 4 cm

    h = 8 cm
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