Given that XY is 28 cm, find the perimeter of the shaded part of the figure. (Use \[\pi =\frac{22}{7}\].)
A) 67 cm
B) 50 cm
C) 80 cm
D) 15 cm
Correct Answer: C
Solution :
Radius of circle\[=\text{28 cm}\div \text{2}=\text{14 cm}\] Area of circle\[=\frac{22}{7}\times 14cm\times 14\,cm\] \[=\text{ 616 c}{{\text{m}}^{\text{2}}}\] Radius of semicircle \[=\text{14 cm}\div \text{2}=\text{7 cm}\] \[\therefore \] Shaded area\[=3\times \frac{1}{2}\times \frac{22}{7}\times 7\times 7=231\,c{{m}^{2}}\] \[\Rightarrow \]\[\text{616 c}{{\text{m}}^{\text{2}}}-\text{ 231 c}{{\text{m}}^{\text{2}}}\text{ }=\text{ 385 c}{{\text{m}}^{\text{2}}}\] Perimeter of shaded part of figure \[=7+7+3\times \left( \frac{1}{2}\times \frac{22}{7}\times 14 \right)\] \[=14\,cm+66\,cm=80\,cm\]
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