How Much Paint for a Hemispherical Dome Using Differentials?

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To estimate the amount of paint needed for a hemispherical dome with a diameter of 54 m, the surface area formula for a hemisphere, 2πr², is applied. Using differentials, the change in surface area (dy) is calculated as dy = 4πr dx, where r is the radius. Substituting the radius (27 m) and the thickness of the paint (0.05 m), the calculation yields dy = 16.96 m². It's important to ensure all measurements are in the same units, as the thickness was initially given in centimeters. The final estimate for the amount of paint required is based on this differential calculation.
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Homework Statement



Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 54 m.

Homework Equations



dy=dy/dx *dx

Surface area of a hemishpere=2pi*r^2

The Attempt at a Solution



dy=4pi*r dx
dy=4pi*27 *.05
dy=16.96
 
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You want to express all of your numbers in the same units. 0.05 cm is not the same as 0.05 m.
 
genius...thank you!
 

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