The topic requires you to calculate the amount of paint with a thickness of 0.07 cm on the hemispherical vault with a radius of 15 m through linear approximation, which is actually an estimate of the volume.

The basic formula of linear approximation is f (x) ~ = f (a)+f' (a) * Δ x, but what this question requires is only the redundant part, that is, the volume of paint, that is, f' (a) * Δ x.

The volume formula of hemisphere: V = 2/3 π r 3, then V' = 2 π r 2.

v(a)*δx=2π* 15^2*0.0007=63/200π~=0.99(m^3)=9.9* 10^5(cm^3))

Therefore, the amount of paint calculated in cubic centimeters is 9.9 *10 5 cm 3.

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