# A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side a metres by a rope of length 5a/2 metres in a grass field. (The cow cann

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A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side a metres by a rope of length 5a/2 metres in a grass field. (The cow cannot graze inside the fenced area.) What is the maximum possible area of the grass field to which the cow has access to graze ?
A. 5 pi a^(2)
B. (5)/(2)pia^(2)
C. 6 pi a^(2)
D. 3pia^(2)

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Correct Answer - A

"Area"=2[(120)/(360)xxpi((5a)/(2))^(2)+(60)/(360)xxpi((3a)/(2))^(2)+(60)/(360)xxpi((a)/(2))^(2)]
=(2 pi)/(3) [(25a^(2))/(4)+(9a^(2))/(8)+(a^(2))/(8)]
=(2pi)/(3)xx(30a^(2))/(4)=5 pi a^(2)