wiz-icon
MyQuestionIcon
MyQuestionIcon
6
You visited us 6 times! Enjoying our articles? Unlock Full Access!
Question

In each of the figures below, find the area of the shaded part

Open in App
Solution

(i)

Central angle = 40°

Radius (r) of the circle = 5 cm

Area of the sector =

=

Area of the shaded part = Area of the sector


(ii)

Central angle = 60°

Radius (r) of the circle = 6 cm

Area of the sector =

=

= 6π cm2

Area of the circle = π r2

= π (6)2 cm2

= 36π cm2

Area of the shaded part = Area of the circle Area of the sector

= (36π 6π) cm2

= 30π cm2


(iii)

Central angle = 60°

Radius (r) of the circle = 7 cm

Area of the sector =

=

In ΔAOB, OA = OB = 7 cm

⇒ ∠OBA = OAB (Angles opposite to equal sides are equal in measure.)

Using angle sum property in ΔAOB:

OBA + OAB + AOB = 180°

2OBA + 60° = 180°

2OBA = 120°

⇒ ∠OBA = 60°

∴ ΔOAB is an equilateral triangle.

Area of the equilateral triangle =

Area of the shaded part = Area of the sector Area of the equilateral triangle

= (25.65 − 21.19) cm2

= 4.46 cm2


(iv)

Radius of the bigger circle = 6 cm

Radius of the smaller circle = 5 cm

Central angle made by the arcs = 120°

Area of the bigger sector =

=

= 12π cm2

Area of the smaller sector =

Area of the shaded part = Area of the bigger sector Area of the smaller sector

= (12π 8.33π) cm2

= 3.67π cm2n

= (3.67 × 3.14) cm2

= 11.52 cm2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Area of a Triangle - by Heron's Formula
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon