There is a cirkle with radius = 1 m. We make fast a rope with agoat to this cirkle. How long is a rope to half of area of cirkle is grazed up?
By Frantisheik
2006-08-30 08:19:15 · 4 answers · asked by frantisheik 1 in Science & Mathematics ➔ Mathematics
i'am not sur i have well understood... but r = 1 / sqrt(2) ?
2006-08-30 08:24:33 · answer #1 · answered by Maverick 5 · 0⤊ 0⤋
Okay, I'm not entirely sure about the question, but I'm going to assume that you want to tie a goat to a rope anchored at the center of a circle of radius one meter, and you want the rope to be long enough to give the goat access to half of that. Therefore all you need is the length of the radius of a circle that encompasses half of pi(1)^2 square meters, or pi/2 square meters. Since the formula for the area of a circle of raduis r is pi(r)^2, this means that r^2 must equal 1/2, and therefore r is sqrt(2)/2 meters. Now, this is kind of annoying, as that number is not rational, but neither is the amount of area you want to enclose (half of pi). So meh. Anyhoo, if you got lazy and skipped all of that longwinded text to get to the answer, the length of the rope should, again, be sqrt(2)/2 meters long.
Please forgive me if my assumptions about the question were incorrect.
2006-08-30 15:28:30 · answer #2 · answered by guywithbadusername 2 · 0⤊ 0⤋
If the goat is tied up to the middle of the circle, the rope would have to be .707 meters long (that's (1/2)â2)
Doug
2006-08-30 15:24:03 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
Oh Frantisheik, is that English ?
2006-08-30 15:36:09 · answer #4 · answered by a_ebnlhaitham 6 · 0⤊ 0⤋