I do not know how to find the radii of a sector in a circle if the sector has a perimeter of 7cm and an area of 3sq.cm
2007-09-02 17:49:58 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
set up simultaneous equations
0.5 X R X R X sector angle = 3
2R + (R X Sector Angle) = 7
solve for R
2007-09-02 17:59:35 · answer #1 · answered by adrian r 2 · 0⤊ 0⤋
Let r = radius of the circle
f = fraction of the circle that make up the sector.
Perimeter = 2 pi r f + 2r = 7
Area = pi r^2 f = 3 pi f = 3/r ^ 2
by substitution
6/r + 2r = 7
2 r^2 - 7r + 6 = 0
(2r -3)(r-4)=0
r = 3/2 or 4
2007-09-02 18:05:30 · answer #2 · answered by norman 7 · 0⤊ 0⤋
you are able to desire to artwork out the fraction of the section/perimeter that's contained interior the international. it is, handily, the ratio of the attitude on the centre of the international to the entire attitude (360 stages). i.e. if P=perimeter of circle p=arc of sector, A and a are comparable for section, then: p/P=a/A=40/360=a million/9. So now all you are able to desire to do is calculate A=pi*r^2, and P=2*pi*r, and remedy the equations p/P=a million/9 & a/A=a million/9 to discover p and a. ascertain you upload two times the radius to p to get the entire perimeter of the international. solid success :)
2016-11-14 01:24:23 · answer #3 · answered by weberg 4 · 0⤊ 0⤋
Perimeter: 2r + x2πr = 7
2r + x2πr - 7 = 0
Area: xπr² = 3
xπr² - 3 = 0
2r + x2πr - 7 = xπr² - 3
xπr² - 2r(1 + xπ) + 4 = 0
Oh, boy...I'm lost.
2007-09-02 18:02:49 · answer #4 · answered by gebobs 6 · 0⤊ 0⤋
http://www.coolmath.com/reference/circles-geometry.html#The_area_of_a_sector_of_a_circle
2007-09-03 03:32:33 · answer #5 · answered by Snoopy 3 · 0⤊ 0⤋