The following diagram shows a circle of centre O, and radius 15 cm. The arc ACB
subtends an angle of 2 radians at the centre O.
B
15 cm
2 rad
Diagram not to scale
AÔB - 2 radians
OA = 15 cm
(a) Find the length of the arc ACB;
(b) Find the area of the shaded region.
Answers
Answer:
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Given :
a circle of centre O, and radius 15 cm. The arc ACB
subtends an angle of 2 radians at the centre O.
To Find : the length of the arc ACB;
the area of the shaded region.
Solution:
π radians = 180°
=> 1 radian = 180°/π
=> 2 radian = 360°/π
length of the arc ACB = ( Angle in deg / 360°) 2 π r
r = 15 cm
= ( 360°/π360°) 2 π * 15
= 30 cm
the length of the arc ACB = 30 cm
Remaining angle = 360° - 360°/π
= 360°(π - 1)/π
area of the shaded region. = (angle in deg / 360°) πr²
= ( 360°(π - 1)/π360°) π(15)²
= 225 (π - 1)
area of the shaded region. = 225 (π - 1) cm²
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