A) 336
B) 259
C) 154
D) 77
Correct Answer: B
Solution :
Area grazed by all cows \[=\frac{180{}^\circ }{360{}^\circ }\pi {{r}^{2}}=\frac{\pi {{r}^{2}}}{2}\] \[=\frac{1}{2}\times \frac{22}{7}\times 7\times 7=77\,\,\text{sq}\,\,\text{m}\] Semi-perimeter of triangular field (s) \[=\frac{26+28+30}{2}=42\,\,\text{m}\] \[\therefore \]Area of the field \[=\sqrt{s\,\,(s-a)(s-b)s-c)}\] \[=\sqrt{42\,\,(42-26)(42-28)(42-30)}\] \[=\sqrt{42\times 16\times 14\times 12}=336\,\,\text{sq}\,\,\text{m}\] \[\therefore \]Area ungrazed by the cows \[=336-77=259\,\,\text{sq}\,\,\text{m}\]
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