What is the perimeter of a sector of angle 45° of a circle with
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    An arc of a circle is of length 5π cm and the sector it bounds has an area 20π cm2. Find the radius of the circle.
    We know that
    Area of a sector bounded by a given arc equals 1 half x (length of a given arc) × radius of a circle
    rightwards double arrow space space straight A space equals space 1 half lr space rightwards double arrow space 20 straight pi space equals space 1 half space straight x space 5 straight pi space straight x space straight r rightwards double arrow space space straight r space equals space fraction numerator 40 straight pi over denominator 5 straight pi end fraction equals space 8 space cm
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    A chord of a circle of radius 14 cm subtends 60° at the centre. Find the area of the major sector.
    Here, r = 14 cm and ∠AOB = 60°
    therefore Area of major sector = Area of the circle - Area of minor sector

    equals space πr squared minus fraction numerator 60 degree over denominator 360 degree end fraction xπr squared equals space open parentheses 1 minus 1 over 6 close parentheses space πr squared equals space 5 over 6 straight x 22 over 7 straight x space 14 space straight x space 14 space cm squared equals space 1540 over 3 equals 513 1 third space cm squared

    Here, r = 14 cm and ∠AOB = 60° Area of major sector = Area of the
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    What is the perimeter of a sector of angle 45° of a circle with radius 7 cm ? [Use π = 22/7].  

    The arc of length l = AB of a sector of angle 45° in a circle of radius 7 cm is given by

    The arc of length l = AB of a sector of angle 45° in a circle of rad

    straight l space equals space straight theta over 360 space straight x space 2 πr space equals space open parentheses 45 over 360 straight x space 2 space straight x space fraction numerator 22 over denominator 7 space end fraction space straight x space 7 close parentheses space cm equals space 5.5 space cm
    therefore Perimeter of sector (OAB)
    = OA + OB + arc AB
    = (7 + 7 + 5.5) cm = 19.5 cm
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    In the following figure, the length of an arc AB = 20π cm is a sector of a circle, find the radius of the circle.
    The arc of length AB = 20π cm of a sector of an angle 144° in a circle of radius r cm is given by

    1 space equals space straight theta over 360 straight x space 2 πr rightwards double arrow space space 20 straight pi space space equals space 144 over 360 straight x space 2 straight pi space straight x space straight r rightwards double arrow space space 20 straight pi space space equals space 2 over 5 space straight x space 2 straight pi space straight x space straight r space rightwards double arrow space space space straight r space space equals space 25 space cm.
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    A chord of a circle of radius 14 cm subtends a right angle at the centre. What is the area of the minor sector?

    Here,   r = 14 cm
    and  angle AOB space equals space 90 degree
    therefore space Area of minor sector

    equals fraction numerator 90 degree over denominator 360 degree end fraction straight x space πr squared equals 1 fourth straight x 22 over 7 straight x 14 straight x 14 equals space 154 space cm squared

    Here,   r = 14 cmand   Area of minor sector

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