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[SOLVED] estimate the amount of paint needed to apply a coat of paint 0.05 cm thick

karush

Well-known member
Jan 31, 2012
2,716
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 \(\displaystyle 50\text{ m}\)

$$\displaystyle
V_h=\frac{1}{2}
\cdot\frac{4}{3}\pi\text{r}^3
\text{ = }
\frac{4}{6}\pi\text{r}^3
$$

$$
dV_h = 2\pi\cdot r^2\cdot \text{dr}
$$

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 $$r=2500.05\text{ cm}$$

my first try at this so....(Wondering)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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.
 

DreamWeaver

Well-known member
Sep 16, 2013
337
(Rock)

Great thread! lol


[I'm a painter and decorator, see, so I might just find a use for this... (Hug) ]
 

karush

Well-known member
Jan 31, 2012
2,716
well a hemisphere would not be easy to paint especially .05 cm uniformly!!

with a big brush I guess :cool:
 

DreamWeaver

Well-known member
Sep 16, 2013
337