? asked in Science & MathematicsMathematics · 1 decade ago

A sector of a circle of radius 8cm has an angle of theta radians. The perimeter of the sector is 30cm?

Find the area of the sector

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  • 1 decade ago
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    Draw a circle.

    Show

    i) Sector containing angle theta, and label the radius 8

    ii) Shade in the pie-shaped sector

    Here's the logic:

    This circle has Area=(pi)r^2

    Area=(pi)8^2

    Area=64(pi)

    The sector's Perimeter is 30

    Since the two arms of the sector are radii, and since each radii=8,

    Length of sector's arc=30-(8+8)

    Arc=30-16

    Arc=14

    Now, Circumference of the circle=(pi)d

    C=(pi)2r

    C=16(pi)

    Therefore the ratio of the arc to the circumference= 14/16(pi), or 7/(8pi)

    The area of the sector is thus 7/(8pi) of 64(pi)

    7/(8pi) / 64pi

    =7/8pi X 64pi/1

    =7 X 8

    =56 cm^2

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