Let's show it by using actual numbers.
Suppose the field is 300m by 300m
area of field is 90000 m^2
area of largest circle = pi(150^2) = 22500pi = 70686 m^2
so area left not sprinkled = 19314 m^2
If we arrange the 9 smaller sprinklers in a pattern like a game of X's and O's
then each radius is 50
and each circle has an area of pi(50^2) = 7853.98
so 9 of those would give us 70686
THE SAME, WOW
The question remains, "Can the 9 circles be arranged so that their radius would be increased" ?
I have no clue how to answer this question.
A farmer has a square plot of land. An irrigation system can be installed with the option of one large circular sprinkler, or nine small sprinklers. The farmer wants to know which plan will provide water to the greatest percentage of land in the field, regardless of the cost and the watering pattern. What advice would you give?
1 answer
1 answer