Folding table

The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase?
The result round to one-hundredths.

Correct result:

p =  67.32 %

Solution:

$$\begin{gathered} S=168{\text{dm}}^2 \\ a=14\text{ dm } \\ S=a\cdot b \\ b=S\mathrm{/}a=168\mathrm{/}14=12\text{ dm } \\ r=b\mathrm{/}2=12\mathrm{/}2=6\text{ dm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{dm}}^2 \\ p=100\cdot {\displaystyle \frac{S_1}{S}}=100\cdot {\displaystyle \frac{113.0973}{168}}=67.32\mathrm{\%} \end{gathered}$$

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