Question

use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.1 cm thick to a hemispherical dome with a diameter of 80 meters. cubic centimeters question help: message instructor submit question jump to answer

Explanation:

Step1: Convert units

The radius of the hemispherical dome \(r = \frac{80}{2}\text{ m}=40\text{ m} = 4000\text{ cm}\). The formula for the volume of a hemisphere is \(V=\frac{2}{3}\pi r^{3}\). The differential of \(V\) with respect to \(r\) is \(dV = 2\pi r^{2}dr\).

Step2: Substitute values

We know that \(r = 4000\text{ cm}\) and \(dr=0.1\text{ cm}\). Substitute these values into the formula \(dV = 2\pi r^{2}dr\).

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Answer:

\(3200000\pi\approx 10053096.49\) cubic centimeters