A running track in the shape of a annulus...the running track has an area of 1000m squared the width of the track is 10m what is the radii of the circles forming the edges of the track???? plz help bin tryin ages and am lost!!!!
2006-11-22 09:28:52 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Engineering
An annulus is just a ring shape.
Let the radius of the inside ring be 'x' and the radius of the outside ring then becomes 'x+10'.
The area of the track is the area of the large circle minus the area of the small circle,
i.e Pi[(x+10)^2-x^2] = 1000
You can whittle this down to x = 50/Pi - 5
So the smaller circle had radius 10.92 (to 2 dp) & the larger circle has radius 20.92 (to 2 dp)
2006-11-22 09:59:47 · answer #1 · answered by saljegi 3 · 1⤊ 0⤋
Pretty easy; this is a case of 2 simultaneous equations (one quadratic and the other linear):
Let the radius of the bigger circle be R
the radius of the smaller circle be r
Formula for area of a circle is A = Pi * r^2 (pi times the radius squared)
The area of the bigger circle minus the area of the smaller circle is equal to the area of the track (mathematically):
(Pi)R^2 - (Pi)r^2 = 1000 sq.m. ---------------(1) our 1st equation
We know that the width of the track is 10 m, mathematically speaking:
R - r = 10 m ----------------------(2) our 2nd equation
solving them simultaneously, we have:
R - r = 10
R = 10 + r -------------------------(3)
(Pi)R^2 - (Pi)r^2 = 1000
From (3), we see that R = 10 + r, so substituting this value in (1)
- (Pi)(10+r)^2 - (Pi)r^2
- (Pi) (100 + 20 r) = 1000 proceeding logically, you end up with
- r = 10.9 m (1dp)
substituting this value in (3)
you have R = 20.9 m (1dp)
So there you go, the radius of the bigger circle is 20.9 m and that of the smaller circle is 10.9 m.
Reminder = the value of Pi is 3.14 (2 sf) and I couldn't put the right symbol of Pi because my keyboard does not have it but i'm sure you know what Pi is.
I hope this has been enlightening, for any more clarification, just post another question and I'd be glad to answer you.
2006-11-22 10:10:38 · answer #2 · answered by Makaveli007 5 · 1⤊ 0⤋
Annulus just means a ring I think so its a matter of working out the radii by transposing the formula for the area of a circle for both radii and producing an equation that matches the question.
2006-11-22 09:52:29 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Area of Annulus = Area of Circle a - Area of circle b
A = (pia^2) - (pib^2)
we can say that a = b + 10
A = (pi(b + 10)^2) - (pi x b^2)
A = pi(b^2 + 20b + 100) - pib^2
A = pib^2 + 20pib + 100pi - pib^2
A = 20pib + 100pi
1000 = pi(20b + 100)
(1000/pi - 100)/20 = b
b = 10.9
a = 20.9
to check we'll put these numbers into our original equation, and we get approx 1000. This is due to rounding our numbers.
2006-11-22 10:13:12 · answer #4 · answered by Andrew H 2 · 1⤊ 0⤋
it can't be a real running track and it cant work.....the 20m of track width can't fit on a area as small as 1000m sq. across the width of the track as the width of the entire stadium is 20m. the answer is 0.
2006-11-22 09:56:45 · answer #5 · answered by Anonymous · 0⤊ 1⤋
You're lost? I don't even know what an annulus is! (I know this doesn't help you, but hope it made you smile. Good luck).
2006-11-22 09:38:23 · answer #6 · answered by Athene1710 4 · 0⤊ 1⤋
Check this out very close to 10.93 and 20.93
Dont have a clue how you calculate cause i dont think you have sufficient information. Youve got me started now but i dont remember high calculus to well.
http://www.mathopenref.com/annulusarea.html
2006-11-22 10:18:14 · answer #7 · answered by Anonymous · 0⤊ 1⤋
I rrly dont understand the queswtion
2006-11-22 09:48:29 · answer #8 · answered by Anonymous · 0⤊ 1⤋
Better be careful you dont run up your own a##se then! lol
2006-11-22 09:31:54 · answer #9 · answered by mistickle17 5 · 0⤊ 2⤋
EACH CIRCLE IS DIFFERENT YOU WOULD NEED SOMEONE WHO IS VERY GOOD AT MATHS
2006-11-22 09:32:11 · answer #10 · answered by Anonymous · 0⤊ 2⤋