- Thread starter
- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 2,870

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....