The perimeter of a sector of a circle, of area 64 pie sa. Cm, is 56 cms. Find the area of sector?
Answers
Answered by
96
Area of circle = 64 pi
=> pi r^2 = 64 pi
=> r^2 = 64
=> r = 8
Radius of circle = 8 cm
Now,
Perimeter of sector = 56
=> 2 × Radius + Length of arc = 56
=> 2 × 8 + Length of arc = 56
=> Length of arc = 56 - 16
=> Length of arc = 40 cm
=> 2 pi R ( theta / 360) = 40
=> 2 × pi × 8 × ( theta) / 360 = 40
=> Theta = 40 × 360 / 16 pi
=> Theta = 5 × 180 / pi
Now,
Area of sector = pi r^2 ( theta / 360)
= pi × 8 × 8 × ( 5 × 180 / pi ) / 360
= 64 pi ( 900/ pi) / 360
= 64 pi × 900 / 360 × pi
= 64 × 900 /360
= 64 × 10 / 4
= 16 × 10
= 160 cm^2
=> pi r^2 = 64 pi
=> r^2 = 64
=> r = 8
Radius of circle = 8 cm
Now,
Perimeter of sector = 56
=> 2 × Radius + Length of arc = 56
=> 2 × 8 + Length of arc = 56
=> Length of arc = 56 - 16
=> Length of arc = 40 cm
=> 2 pi R ( theta / 360) = 40
=> 2 × pi × 8 × ( theta) / 360 = 40
=> Theta = 40 × 360 / 16 pi
=> Theta = 5 × 180 / pi
Now,
Area of sector = pi r^2 ( theta / 360)
= pi × 8 × 8 × ( 5 × 180 / pi ) / 360
= 64 pi ( 900/ pi) / 360
= 64 pi × 900 / 360 × pi
= 64 × 900 /360
= 64 × 10 / 4
= 16 × 10
= 160 cm^2
Answered by
20
Answer:
the area of the given sector is 160sq.cm.
Step-by-step explanation:
Is given in the attachment (image)
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