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Calculus

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Use linear approximation or differentials to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.010000cm thick to a hemispherical dome with a diameter of 75.000meters.

  • Calculus -

    V=(4/3)πr³
    dV/dr=4πr²
    Approximate dV/dr with
    ΔV/Δr, we get
    ΔV=4πr²Δr
    where
    r=75.000/2, and
    Δr=0.0001m after conversion to metres.

  • Calculus - correction -

    Here's the same answer in the correct units (cubic centimetres).
    V=(4/3)πr³
    dV/dr=4πr²
    Approximate dV/dr with
    ΔV/Δr, we get
    ΔV=4πr²Δr (in cubic cm)
    where
    r=75.000/2*100 cm
    =3750 cm, after conversion to cm
    Δr=0.01cm

  • Calculus -

    Actually, the formula for the volume of a HEMIsphere is (4/6)pi(r)^2

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