the area of a sector of a circle of radius 8cm is 16πsq. cm. find the length of the corresponding arc
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see in photo length of arc is 12.57cm
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Data:
Radius = r = 8 cm
Area = A = 16 cm²
Length of an arc = L = ?
Solution:
The length of arc is given by the formula as
L = 2πrΘ / 360 .......... (1)
First we calculate the value of Θ
Since,
Area = A = πr²Θ/360
Putting the values, we get:
16 = (3.14) (8)² Θ / 360
16 = 200.96 Θ / 360
16x360 = 200.96 Θ
5760 = 200.96 Θ
Θ = 5760/200.96
Θ = 28.66
Now put this value in equation (1), we get:
L = 2πrΘ / 360
L = 2(3.14)(8)(28.66) / 360
L = 3.99 cm
which is the required answer. Hopefully its helpful. Thanks.
Radius = r = 8 cm
Area = A = 16 cm²
Length of an arc = L = ?
Solution:
The length of arc is given by the formula as
L = 2πrΘ / 360 .......... (1)
First we calculate the value of Θ
Since,
Area = A = πr²Θ/360
Putting the values, we get:
16 = (3.14) (8)² Θ / 360
16 = 200.96 Θ / 360
16x360 = 200.96 Θ
5760 = 200.96 Θ
Θ = 5760/200.96
Θ = 28.66
Now put this value in equation (1), we get:
L = 2πrΘ / 360
L = 2(3.14)(8)(28.66) / 360
L = 3.99 cm
which is the required answer. Hopefully its helpful. Thanks.
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