Question #cd663

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Question #cd663

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Answer 1 · 2016-10-02T13:35:17

$115$ $115$ pots can be painted completely

Explanation:

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

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

$radius = 15 c m = 0.15 m and height 20 c m = 0.2 m$ $"radius " = 15cm = 0.15m and "height "20cm = 0.2m$

Once we know the surface area of 1 pot, we can just divide $30 m^{2}$ $30m^2$ 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 = $π r^{2}$ $pir^2$ Curved surface area = $2 π r h$ $2pirh$

Total outside area of one pot = $π r^{2} + 2 π r h$ $pir^2 + 2pirh$

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

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

$\frac{30}{0.0825 π} = 115.749$ $30/(0.0825pi) = 115.749$

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 $\frac{3}{4}$ $3/4$ of the next pot gets done.

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Question #cd663

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