Ab and CD are respectively arcs of two concentric circles of radii 21cm and 7cm and o centre If angleAOB is 30 then find the area of the shaded region
Answers
Answer:
Explanation:
Ans--1350cm.sq.
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