# 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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