A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take (pi = frac{22}{7})]
-
A.
170(^o) -
A.
192(^o) -
B.
177(^o) -
C.
182(^o)
Correct Answer: Option B
Explanation
Length of arc, L = 21.4 – 2 x 4.2cm
= 21.4 – 8.4
= 13cm
But L = (frac{theta}{360^o}) x 2(pi r)
i.e 13 = (frac{theta}{360^o}) x 2 x (frac{22}{7}) x 4.2
= 13 x 360(^o) x 7
= (theta) x 2 x 22 x 4.2
(theta) = (frac{13 times 360^o times 7}{44 times 4.2})
= (approx) 177.27(^o)
(approx) 177(^o) (to the nearest degree)