Ms. Jabbour's rectangular yard is to be used for the Easter egg hunt this year. The yard is 30 feet wide, 40 feet long and has two 3-foot wide cement paths as shown in the diagram. Her dog Franky is tied to one corner with a 6-foot long leash (assume that Franky cannot reach the cement paths). What is the maximum possible area in which the eggs can be placed if they cannot be placed on the cement walkways or where Franky can reach? (Due March 28, 2008)
5 comments:
Answer = 999-36(pi)
First I found the area of the circle which is (pi)r^2 and got 36(pi). Then found the area of both walkways using 3x40 and 3x30 and got a total of 210 but there's a part that overlaps with an area of 3x3=9. So I subtracted that from 210 getting 201. Finally I found the area of the overall rectangle getting 30x40=1200 then subtracted 201 getting 999. So the answer is 999-36(pi).
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woops the answer i got is 999-9(pi) now that i look at it
970.725666117692 square feet.
Solution:
Move the paths to the edges of the yard so that the grassy area is in the shape of a rectangle with dimenstions 27x37.
Area of rectangle = L x W
Area of circle = pi(r)^2
27x37=999 sq. ft.
6^2(pi) = 36(pi)
36(pi)/4 = 9(pi) sq. ft.
999 - 9(pi) = 999 - 28.27433388
= 970.7256661 sq. ft.
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