question_answer

  Four cows are tied at the four corner of the square field of side \[20\text{ }m,\]so that they can just reach to each other. What is the area of the field which remain ungrazed?

A)  \[40\text{ }{{m}^{2}}\]                             

B)  \[\text{86 }{{m}^{2}}\]       

C)  \[\text{60 }{{m}^{2}}\]                 

D)  \[\text{172 }{{m}^{2}}\]

Correct Answer: B

Solution :

(b): \[{{C}_{1}}\] to \[{{C}_{4}}\]4 are four cows Ungrazed area = area of square - area of four quarter circles. \[=20\times 20-4\times \frac{\pi }{4}\times {{\left( 10 \right)}^{2}}\] \[=400-100\pi \] \[=100\,(4-\pi )\] \[\approx 86\]