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3 November, 15:23

A cylindrical can, open at the top, is to hold 500 cm3 of liquid. Find the height and

radius that minimizes the amount of material needed to manufacture the can.

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  1. 3 November, 15:34
    0
    Find h with respect to r:

    V = πr²h = 500

    h = 500/πr²

    Plug this into the surface area equation:

    SA = πr² + 2πrh

    = πr² + 2πr (500/πr²)

    = πr² + 1000/r

    Differentiate and set to 0, solve for r:

    dSA/dr = 2πr - 1000/r² = 0

    2πr = 1000/r²

    r³ = 500/π

    r = (500/π) ^1/3

    ≈ 5.42 cm

    find h:

    h = 500/πr²

    = 500/[π (5.42) ²]

    = 5.42cm
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