Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Perimeter & Area of a sector of a circle?

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

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  • 1 decade ago
    Favorite Answer

    set up simultaneous equations

    0.5 X R X R X sector angle = 3

    2R + (R X Sector Angle) = 7

    solve for R

  • norman
    Lv 7
    1 decade ago

    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

  • weberg
    Lv 4
    4 years ago

    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 :)

  • gebobs
    Lv 6
    1 decade ago

    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.

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