- Thread starter
- #1
karush
Well-known member
- Jan 31, 2012
- 2,870
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....
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....
