Calculus Homework

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Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.01cm thick to a hemispherical dome with a radius of 18 meters.

  • Calculus Homework -

    Hemisphere = 1/2 sphere

    V = (2/3)πr^3
    dV/dr = 2πr^2
    dV = 2πr^2 dr
    ∆V = 2πr^2 ∆r
    ∆V = 2π(18^2)(.0001)
    = .0648π
    or
    appr .2036 m^3

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