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Pujan Gor
Pujan Gor asked in Science & MathematicsMathematics · 9 years ago

Volume , surface area of a cylinder?

A chemical factory wishes to make a cylindrical container, of thin metal to hold 10 cm^3, using the least possible area of metal. If the outside surface is S cm^2, and the radius is R cm , show that S=2pieR^2 + 20/r and hence find the required radius and height for the container ( leave pie in the answer)

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  • Como
    Lv 7
    9 years ago

    S = 2πr² + 2πrh

    V = πr²h

    10 = πr²h

    h = 10 / πr²

    S = 2πr² + 2πr (10/πr²)

    S = 2πr² + 20 / r

    S ` (r) = 4π r - 20 / r² = 0

    4π r = 20 / r²

    4π r³ = 20

    π r³ = 5

    r = 1.71 /π cm

    h = 10 / (πr²) = 10 / (π x 1.17²) = 7.31 / π cm

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