Folding table

The folding kitchen table is rectangular 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 answer:

p =  67.32 %

Step-by-step explanation:

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

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