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15 March, 23:45

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)

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  1. 16 March, 00:07
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    Answer: the amount needed is around 25.64m^2

    Step-by-step explanation:

    Here we have a thickness of 0.07cm and a surface of 54m

    So we have the integral of volume between:

    54m and 54m + 0.0007m

    this is equal to:

    v = ∫sin (θ) r^2drdθdφ

    Where dr goes as we know, from 54m to 54m+0.0007m, dφ goes from 0 to 2*pi, and θ goes from 0 to pi.

    Solving the integral, we have that:

    v = 2*pi*∫sin (θ) rdrdθ

    v = 4*pi*∫rdr = (4/3) * pi * ((54.0007m) ^3 - 54m^3) = 25.64m^3
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