The diagram shows a sector of a circle , centre o and radius 6cm . the sector angle is 30. the area of the shaded segment is (kπ-c) cm^2 , where k and c are integers. find the value of k and the value of c
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Given : a sector of a circle , centre o and radius 6cm . the sector angle is 30°
area of the shaded segment is (kπ-c) cm²
k and c are integers.
To Find : value of k and the value of c
Solution:
Area of Shaded region = Area of sector - area of triangle
Area of sector = (30/360)πr²
= (1/12)π6²
= 3π cm²
Area of Triangle = (1/2) * 6 * 6 Sin30
= 18 *(1/2)
= 9 cm²
Area of Shaded region = 3π - 9 cm²
Compare with (kπ-c) cm²
k = 3
c = 9
value of k = 3 and the value of c = 9
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