# Question #cd663

Oct 2, 2016

$115$ pots can be painted completely

#### Explanation:

The first problem you should see is that there are two different units.
${m}^{2} \mathmr{and} c m$

Converting units of area is more tricky than just lengths, so let's change $c m$ to $m$ right at the beginning. For $c m \rightarrow m , \div 100$

$\text{radius " = 15cm = 0.15m and "height } 20 c m = 0.2 m$

Once we know the surface area of 1 pot, we can just divide $30 {m}^{2}$ by that answer to find how many of the same pots can be painted.

Each pot has a base ( a circle) and the curved part.
You should know those formulae
Circle Area =$\pi {r}^{2}$ Curved surface area = $2 \pi r h$

Total outside area of one pot =$\pi {r}^{2} + 2 \pi r h$

$S A = \pi {\left(0.15\right)}^{2} + 2 \pi \left(0.15\right) \left(0.2\right)$
$S A = 0.0225 \pi + 0.06 \pi$
$S A = 0.0825 \pi \text{ "m^2" } \leftarrow$ leave it in terms of $\pi$ for now

How many pots can be painted? Divide 30 by the area of one pot.

$\frac{30}{0.0825 \pi} = 115.749$

Now be careful... Although the first decimal is more than 5, do not round up...

This means that 115 pots can be painted completely but only about $\frac{3}{4}$ of the next pot gets done.