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:

S=168 dm2 a=14 dm  S=a b  b=S/a=168/14=12 dm  r=b/2=12/2=6 dm  S1=π r2=3.1416 62113.0973 dm2  p=100 S1S=100 113.0973168=67.32%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 \ \dfrac{ S_{1} }{ S }=100 \cdot \ \dfrac{ 113.0973 }{ 168 }=67.32 \%



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