Come on, get your brains in gear...
I have a peice of Rope 20 metres long, which I place in a circle on the ground.
What is the width of the ground I will need at the widest point of the circle.
10 points if you both get the right answer AND show your working. There may be more than one way to solve it.
2006-08-15 22:03:29 · 27 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
You have till 1300 hours BST to solve it.
2006-08-15 22:04:09 · update #1
Tough choice of answers, so I’ll start by putting you out of your misery.
The rope is in the shape of a circle, which most of you caught on to, but some did jump to the suspicious conclusion that the circle was drawn on the floor. If I had made it simple, it would defeat the morning workout.
So, the 20m rope in a circle translates as the Circumference being 20m. One mark if you twigged that.
I asked for the width of the circle at the widest point. Since a circle is perfect round, the widest point is any straight line through the centre from side to side. Second mark for knowing that. This line is called the diameter. Another mark for that.
The equation that links circumference and diameter is C=pixd, so 1 mark for stating that equation, and another for showing the rearranging; C=pixd, (C/pi)=((pixd)pi), so d=C/pi.
Now to insert the numbers for another mark, C=20, pi= 3.143, and find d, d=(20/3.143). D=6.36 cm. One mark for answer and another for going to 3 digits
2006-08-16 06:04:29 · update #2
20 meters = 2 pi r
20 meters = pi X D
D = 20/pi
6.369
I took pi as 3.14 as I don't have a calculator to hand to get a more accurate result.
2006-08-15 22:10:36 · answer #1 · answered by Anonymous · 2⤊ 0⤋
If I answer this question literally:
You are placing a 20m rope within a circle on the ground.
The circle does not necessarily need to have a circumference of the same length of the rope.
A circle does not have a widest point, it has the same diameter all the way round.
Therefore assuming that the circle is on the ground then the width of the ground needs to be the same as the diameter of the circle and the diameter of the circle is not defined.
However the circle does not necessarily need to be on the ground (only the rope is on the ground) so the circle could be any size and the ground only needs to be large enough to place the rope on without it falling off.
Perhaps your questions should read "I have a piece of rope 20 meters long. I place the rope on the ground to form the shape of a circle.....
Sorry to be picky but the answer is far to simple if one jumps to traditional conclusions about the use of English in the question.
2006-08-15 22:30:07 · answer #2 · answered by Anonymous · 1⤊ 0⤋
You draw a circle on the ground that is 20 metres wide at the widest point, you then place the rope inside that circle. From 1 side of the rope to the other (in a straight line) the length is 20 meters.
Therefore the widest point of the circle is 20 meters.
2006-08-15 22:11:29 · answer #3 · answered by Anonymous · 1⤊ 0⤋
Assuming the circle on the ground has already been drawn, the maximum width you will need is the diameter of the circle (not stated in the question).
If the rope is stretched straight and just fits the circle then the answer is 20m (circle diameter).
If it is the rope that makes the circle then the circumference of the circle is 20m so divide by pi to get the diameter (6.38m). Width needed will be 6.38m.
2006-08-15 22:19:41 · answer #4 · answered by Nothing to say? 3 · 1⤊ 0⤋
Cicumference = 20m
ie 2 pi r = 20
2r = 20 / pi
2r = 20 / 3.14
2r = 6.36m
Thus, the width of the ground at the widest point ofthe circle is 6.36 metres.
2006-08-16 00:20:15 · answer #5 · answered by Anonymous · 0⤊ 0⤋
since rope is curved to form circle, therefor,
circumference = 20 m
2*22/7*r = 20
( where, 22/7 = pi and r =radius of circle)
r = (20*7)/22*2
r =35/11
r =3.45 (approx)
Also minimum width of ground = diameter of circle
= 2 * r
=2* 3.45 = 6.9m <--ans
2006-08-15 22:19:45 · answer #6 · answered by kc 2 · 0⤊ 0⤋
a circle with circumference of 20 meters would have a diameter of ~6.3662 meters, so that's how much ground you would need - 20 ÷ π
i considered the thickness of the rope as possibly being relevant, and inflating that figure a slight bit, but dismissed that. the rope, also being round, would rest on the ground under its center. no extra ground would be needed to support that little round overhang
2006-08-15 22:16:01 · answer #7 · answered by gylbertpenguin 2 · 0⤊ 0⤋
I've had only one cup of coffee so far, so could you translate this to feet and inches for this Yank? Hehee, just kidding. I'll try again after caffeine II.
Could you specify the thickness of the rope? Is it one of those HUGE 10 inch/25cm ropes used on ships, or it is a piece of clothesline?
2006-08-15 22:17:47 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Circumference=20 m
Pi =3.142
Diameter =20/3.142
=6.4 m this is the width of the ground at the wid
est point of the circle.
2006-08-15 23:33:40 · answer #9 · answered by mamanoelia 3 · 0⤊ 0⤋
2*22/7*R=20 R=radius of circle
22/7*R=10
r=10*7/22=3.1818181818..
Now the radius we have
so double of radius is2*3.181818
this is 6.363636....
So this is an approximate width of that ground.
I assumed this ground as a quadrilateral so this is right for a quadrilled where the parallel side are equal
2006-08-15 22:20:52 · answer #10 · answered by P5 2 · 0⤊ 0⤋