suppose a belt tightly stretched about the equator of the earth just fits. How long a piece should be inserted so that the belt could encircle the earth at a distance of 1 m away from the equator at all points? how do i do this, explain it please??
2006-07-07 10:43:19 · 14 answers · asked by 12345 1 in Science & Mathematics ➔ Mathematics
whats the answer?
2006-07-07 10:49:09 · update #1
2π meters
Assume that the radius of the Earth is r, and the belt fits tightly around it. Therefore the length of the belt is 2πr. Now raise it 1 meter above the surface (thus add 1 meter to the radius). The new length would be 2π(r+1). The difference in these two lengths is 2π(r+1)-2πr=2π(r+1-r)=2π. Thus you needed to add 2π meters to the belt.
2006-07-07 10:48:25 · answer #1 · answered by Eulercrosser 4 · 1⤊ 0⤋
first of all find out the diameter of the earth, I`ll let you do this bit. If you find the radius then just double that to get the diameter.
Let d=diameter
1st belt = pi x d
2nd belt = pi x (d+2 meter)
the reason 2 is used not 1 is because increasing radius by 1 is the same as increasing diameter by 2
make sure that you get the diameter measured in meters, not kilometers. Simply multiply by 1000 to convert kilometers to meters.
The piece you need to insert will be the 2nd belt minus the 1st belt
= (pi x (d+2)) - (pi x d)
= 2 x pi
notice that the answer doesn`t depend on the size of the earth, so any size planet would require the same addition to go around the planet at 1 meter high.
by the way 2 x pi = 6.283185 meters.
2006-07-07 10:58:11 · answer #2 · answered by MARTIN B 4 · 0⤊ 0⤋
The length of the belt is the circumference of the earth. Circumference is equal to 2*pi*radius. If you want to have the belt a distance 1 m away from the surface, you're making a new circle with a radius 1 greater than before. To find the length of the belt piece you insert, find the difference of the two numbers.
Let's call the radius of the earth r. The length of the belt is 2*pi*r. The length of the belt with the insert is 2*pi*(r+1). The difference is 2*pi*(r+1) - 2*pi*r = 2*pi. The length you insert is 2*pi
2006-07-07 10:49:56 · answer #3 · answered by Phil 5 · 0⤊ 0⤋
Since the diameter of the earth is 12,756.32 kilometers, or 12,756,320 meters, you would have a circle (or belt) with a diameter of 12,756,320 meters. Then you would add 2 meters to this to get a circle that is 1 meter wider on all sides, which would give a total diameter of 12,756,322 meters. To convert diameter (distance across widest part of the circle) to circumference (the length of the stretched out belt) just multiply Pi and the diameter.
Pi = 3.1416
Old diameter = 12,756,320 meters
Old circumference = 3.1416 * 12,756,320m = 40,075,254.9120 m
Now find the new circumference:
Pi = 3.1416
New diameter = 12,756,322 meters
New circumference = 3.1416 * 12,756,322m = 40,075,261.1952
Now take the new belt length (New circumference) and subtract the old belt length (Old circumference) from it:
40,075,261.1952 m - 40,075,254.9120 m = 6.2832 meters
So the length of the new piece to be inserted is 6.2832 meters.
2006-07-07 11:15:07 · answer #4 · answered by Anonymous · 0⤊ 0⤋
So as per ur inputs radius of thebelt is the radius of earth in metres "R" ( 6,378.135 km) . If you want that belt should encircle the earth at a distance 1m away frm the equator at all points, now the new radius of the belt will be = (1+R)
length of the new belt will be =2*Pi*(R+1)= 2*Pi*R+2*Pi
2006-07-07 10:51:48 · answer #5 · answered by naika_m 2 · 0⤊ 0⤋
This is an application of the difference of the circumference of two circles.
#1 The first one were the belt tightly fits is 2πr
the 2π would something like 2(3.14159) [3.14159 is an approximation of π]
the r would be the radius of the earth
#2 Then you would find the second circumference which would be 2π(r + 1meter)
#3 Then you subtract the two
[2π(r + 1meter)] - (2πr)
Play a little with the equation
2π[(r + 1meter) - r]
2π[r + 1meter - r]
2π[r - r + 1meter]
2π[1meter]
That will get you the extra length you would have to add to the belt
2006-07-07 10:53:11 · answer #6 · answered by CR 4 · 0⤊ 0⤋
If you are doing calculus, there is a quick way to approximate the answer using differentials...
1) C = pi * d
you want to know the change in circumference/length of the belt, so using differentials:
2) dC = pi * dd, or change in circumfrence equals pi times change in diameter. Since the radius is changing by 1m, the diameter changes by 2m, so you have...
3) dC = 2*pi m
The change in circumference is approximately 2 pi meters.
2006-07-07 11:12:02 · answer #7 · answered by Anonymous · 0⤊ 0⤋
circumference = 2 * pi * radius;
This can be differentiated to give:
change in circumference = 2*pi*change in radius.
you are proposing a change in the radius of 1m.
Therefore the change in the circumference is 2*pi*1m = 6.28m
ANSWER: make this belt 6.28 m longer and then you can suspend it above the equator at a height of 1m above the ground all around the earth.
I know, it is a rather surprising answer.
2006-07-07 10:50:34 · answer #8 · answered by Anonymous · 0⤊ 0⤋
increase the radius from center of earth to the belt by 1m and then use the circumference equation 2pier (I thnk) to find the circumference
2006-07-07 10:48:25 · answer #9 · answered by Anonymous · 0⤊ 0⤋
what is the diameter of the earth? Add 2 meters to that...Find out the circumference to the new diameter...
2006-07-07 10:47:30 · answer #10 · answered by Fox 34 4 · 0⤊ 0⤋