Question

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see the given figure). If∠AOB = 30°, find the area of the shaded region.

Answer 1

Sector of a circle:
The region enclosed by two radio & the corresponding arc of a circle is called the sector of a circle.

The sector contain minor sector and major sector.

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Solution:

[Fig is in the attachment]

Given:

∠AOB = 30°
Smaller Radius OC (r) = 7 cm
Bigger Radius OB(R)= 21 cm

Angle made by sectors of both concentric circles (thetha) =30°

Area of the larger sector AOB = (30°/360°) × π R² cm²

= 1/12 × 22/7 ×( 21)² cm²

= 693/6 cm²

Area of the smaller sector COD= (30°/360°) × π r² cm²


= 1/12 × 22/7 × 72 cm²

= 77/6 cm²


Area of shaded region= area of sector AOB - area of sector COD

Area of the shaded region =693/6 – 77/6 cm²

= 616/6 cm² = 308/3 cm²

Hence, the area of shaded region is 308/3 cm²

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Hope this will help you.....

Answer 2

Answer:

Step-by-step explanation:

Radius of bigger circle=21 cm and sector angle theta=30°

•°• area of the sector OAB= 30/360×22/7×21×21 cm^2

= 11×21/2= 231/2cm^2

Again,radius of smaller circle

r=7cm

The sector angle is 30° too

•°• Area of the sector OCD=30/360×22/7×7×7= 77/6 cm^2

Area of the shaded region

= 231/2-77/6= 693-77/6= 616/6= 308/3cm^2