I need help with this problem, i dont know how to set it up.

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.02000 cm thick to a hemispherical dome with a diameter of 45.00 meters.

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- Oct 27th 2006, 10:03 AMvietLinear approximation
I need help with this problem, i dont know how to set it up.

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.02000 cm thick to a hemispherical dome with a diameter of 45.00 meters. - Oct 27th 2006, 10:20 AMThePerfectHacker
We have that volume of the hemisphere is a function of the radius, that is,

$\displaystyle V(r)=\frac{2}{3}\pi r^3$

Since $\displaystyle .02$ is a small number we have that the change in the derivative is approximately the change in the actual function, that is,

$\displaystyle dV\approx \Delta V$

Since,

$\displaystyle \frac{dV}{dr}=2\pi r^2$

The change in derivative is,

$\displaystyle dV=2\pi r^2 dr$

Where $\displaystyle dr=\Delta r$ the change in the radius.

Which is, $\displaystyle +.02$

Thus,

$\displaystyle dV=2\pi (45)^2 (.02)$

Thus,

$\displaystyle dV=2\pi (2025)(.02)$

Thus,

$\displaystyle dV=81 \pi$

That means the change in volume is approximately increased by $\displaystyle 81 \pi\mbox{ cm}$