Find the area of shaded region in the figure where the radius of two concentratic circle is 7cm and 5cm angle AoC =30degre Related: Major Minor Sector and Segments - Area Related to Circles, Maths, Class 10

Question

Find the area of shaded region in the figure where the radius of two concentratic circle is 7cm and 5cm  angle AoC =30degre Related:  Major Minor Sector and Segments - Area Related to Circles, Maths, Class 10

Answer

Answer

22/7×7×7×30/360-22/7×5×5×30/360
22/7×1/12(49-25)
11/7×1/6×24
11/7×4
44/7

Answer

Calculation of Shaded Area in Concentric Circles

Given:
- Radius of larger circle (r1) = 7 cm
- Radius of smaller circle (r2) = 5 cm
- Angle AoC = 30 degrees

Finding the Area of the Shaded Region:
To find the shaded area between the two concentric circles, we need to calculate the areas of the sector and the triangle separately and then subtract the area of the triangle from the sector.

1. Area of Sector:
- Area of sector = (θ/360) x πr², where θ is the angle in degrees and r is the radius of the circle
- Area of sector AOC = (30/360) x π x 7²
- Area of sector AOC = (1/12) x 49π
- Area of sector AOC = 4.083 cm²

2. Area of Triangle:
- In triangle AOC, we have two sides as radii of the circles (r1 and r2) and the angle between them as 30 degrees.
- Area of triangle AOC = (1/2) x r1 x r2 x sin(30)
- Area of triangle AOC = (1/2) x 7 x 5 x 0.5
- Area of triangle AOC = 8.75 cm²

3. Calculating Shaded Area:
- Shaded area = Area of sector AOC - Area of triangle AOC
- Shaded area = 4.083 - 8.75
- Shaded area = -4.667 cm²

Conclusion:
The area of the shaded region in the figure is approximately -4.667 cm². Since the calculated value is negative, it indicates that the triangle is larger than the sector in this case.

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