Four identical semicircles are drawn inside a big square as shown in the figure. Each side of the big square is 14 cm long. |
A) \[125\text{ }c{{m}^{2}}\]
B) \[112\text{ }c{{m}^{2}}\]
C) \[173\text{ }c{{m}^{2}}\]
D) \[159\text{ }c{{m}^{2}}\]
Correct Answer: B
Solution :
(b): Radius \[=14\text{ }cm\div 2=7cm\] Area of a \[=\frac{1}{2}\times \frac{22}{7}\times 7\,\,cm\times 7\,\,cm\] \[=38.5\,\,c{{m}^{2}}\] Area of \[=\frac{1}{2}\times 7\,\,cm\,\,\times 7\,\,cm=24.5\,\,c{{m}^{2}}\] Area of a \[=38.5\,\,c{{m}^{2}}-24.5\,\,c{{m}^{2}}\] \[=14\,\,c{{m}^{2}}\] Area of shaded region \[=14\,c{{m}^{2}}\times 8=112\,\,c{{m}^{2}}\] Aliter Refer to Q.-10 again; Area (asked, here) \[=4\times \] standardized area as illustrated in solution to Q.-10. \[=4\times \frac{{{a}^{2}}}{2}[\pi -2]\] (where, a = length of one of the smaller squares)You need to login to perform this action.
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