Question

Q.A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73

Q.An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

plzz anyone explain me this 2 Q's.​

Answer 1

Answer:

ANSWER

In the mentioned figure,

O is the centre of circle,

AB is a chord

AXB is a major arc,

OA=OB= radius = 15 cm

Arc AXB subtends an angle 60o at O.

Area of sector AOB=36060×π×r2

                                    =36060×3.14×(15)2

                                    =117.75cm2

Area of minor segment (Area of Shaded region) = Area of sector AOB− Area of △ AOB

By trigonometry,

AC=15sin30

OC=15cos30

And, AB=2AC

∴ AB=2×15sin30=15 cm

∴ OC=15cos30=1523=15×21.73=12.975 cm

∴ Area of △AOB=0.5×15×12.975=97.3125cm2

∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm2

Area of major segment = Area of circle − Area of minor segment

                                       =(3.14×