Math, asked by ishitakapadia17, 1 month ago

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

Answered by arshwetaapatil
0

Answer:

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Answered by amitnrw
0

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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