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, 11:03 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, 11:20 AMThePerfectHacker
We have that volume of the hemisphere is a function of the radius, that is,

Since is a small number we have that the change in the derivative is approximately the change in the actual function, that is,

Since,

The change in derivative is,

Where the change in the radius.

Which is,

Thus,

Thus,

Thus,

That means the change in volume is approximately increased by