*est amt of paint to a coat of paint 0.05 cm thick

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In summary, the conversation discusses using differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with a diameter of 50 m. The formula for finding the volume of the dome is given, along with an approximation using differentials. The conversation also mentions the difficulty of painting a hemisphere uniformly and references a comedic solution from Mr. Bean.
  • #1
karush
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Use differentials to estimate the amount of paint needed
to apply a coat of paint \(\displaystyle 0.05 \text{ cm}\) thick
to a hemispherical dome with a diameter of \(\displaystyle 50\text{ m}\)
$\displaystyle V_h=\frac{1}{2} \cdot\frac{4}{3}\pi\text{r}^3 = \frac{4}{6}\pi\text{r}^3$
$dV_h = 2\pi\cdot r^2\cdot \text{dr}$
so if $$r=25\text{ m} = 2500\text{ cm}\text { and }dr = 0.05\text{ cm}$$ then
$dV_h = 2\pi \ 2500\text{ cm}^2\cdot 0.05\text{ cm}\approx 1.96\text{ m}^3$
or should $r=2500.05\text{ cm}$
 
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  • #2
You did it correctly. I always like to, if possible, compare the approximate to the true value:

\(\displaystyle V=\frac{2\pi}{3}\left((r+\Delta r)^3-r^3 \right)\)

\(\displaystyle V=\frac{2\pi}{3}\left(2500.05^3-2500^3 \right)\text{ cm}^3\approx1.96353467866359\text{ m}^3\)

This is very close to the estimate.
 
  • #3
(Rock)

Great thread! lol[I'm a painter and decorator, see, so I might just find a use for this... (Hug) ]
 
  • #4
well a hemisphere would not be easy to paint especially .05 cm uniformly!

with a big brush I guess :cool:
 
  • #5
karush said:
well a hemisphere would not be easy to paint especially .05 cm uniformly!

with a big brush I guess :cool:
Only one way to get such even coverage... Mr Bean has the answer: Mr Bean - Painting with Fireworks - YouTube

;)
 

FAQ: *est amt of paint to a coat of paint 0.05 cm thick

1. How do I calculate the estimated amount of paint needed for a coat that is 0.05 cm thick?

The estimated amount of paint needed for a coat that is 0.05 cm thick can be calculated by multiplying the area of the surface to be painted by the paint's coverage rate, which is typically listed on the paint can. This will give you the total volume of paint needed in cubic centimeters.

2. Is there a specific formula for determining the estimated amount of paint needed?

Yes, the formula for calculating the estimated amount of paint needed is: Volume of paint (cm3) = Surface area (cm2) x Paint coverage rate (cm3/cm2)

3. Can the estimated amount of paint needed vary depending on the type of surface?

Yes, the type of surface can affect the estimated amount of paint needed. Different surfaces may require different amounts of paint due to their texture, porosity, and other factors.

4. Are there any other factors that can affect the estimated amount of paint needed?

Yes, other factors that can affect the estimated amount of paint needed include the number of coats desired, the type of paint being used, and the skill level of the painter.

5. How accurate is the estimated amount of paint needed?

The estimated amount of paint needed is an approximation and may not account for any mistakes or variations in application. It is always best to have a little extra paint on hand to ensure complete coverage.

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