SOLUTION: a goat is tied to a corner of a 30 ft by 35 ft building. if the rope is 40 ft long and the goat can reach 1 ft farther than the rope length, what is the maximum area the goat can c

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Question 1178371: a goat is tied to a corner of a 30 ft by 35 ft building. if the rope is 40 ft long and the goat can reach 1 ft farther than the rope length, what is the maximum area the goat can cover?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

IMG-0483

Given:
width of building = ft
length of building = ft
length of rope = ft
total reach of goat = ft
To solve for the total area, get the sum of the three areas.

Area 1 is equal to the one quarter of the area of a ft radius circle.



Area 2 is equals to the one quarter of the area of a ft radius circle.

Area 3 is equals to the three quarters of the area of a ft radius circle.

total area:




Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

The accessible area is the disjoint union of 5 (five, FIVE) 90° circular sectors



 = 


 = 


 = 


 = 


 = .


Therefore, the total accessible area is


    A =  =  = 4084.07 square feet   (rounded).      ANSWER

Solved.



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