find the area of the shaded part where the diameter of the great circle 28cm and the radius of the small circle is 7cm.
Answers
Required Answer :
The area of shaded part = 462 cm²
Given :
→ Radius of greater circle = 28 cm
→ Radius of smaller circle = 7 cm
To find :
→ Area of the shaded part = ?
Concept :
To find the area of shaded part, firstly calculate the radius of the bigger circle and then we will find the area of both the circles having greater and smaller radius. After getting their values, subtract the area of circle having the smaller radius from the greater one, the resultant value will be the area of shaded part.
Formula to calculate the Radius :-
- Radius = Diameter ÷ 2
Formula to calculate area of circle :-
- Area of circle = πr²
Solution :
Radius of bigger circle :-
→ Radius = 28 ÷ 2
→ Radius = 14
Therefore, the radius of bigger circle = 14 cm
Area of bigger circle :-
→ Area = πr²
→ Substituting the given value :-
→ Area = 22/7 × (14)²
→ Area = 22/7 × 14 × 14
→ Area = 22 × 2 × 14
→ Area = 616
Therefore, the area of bigger circle = 616 cm²
Area of smaller circle :-
→ Area = πr²
→ Substituting the given values :-
→ Area = 22/7 × (7)²
→ Area = 22/7 × 7 × 7
→ Area = 22 × 7
→ Area = 154
Therefore, the area of smaller circle = 154 cm²
Area of shaded part = Area of greater circle - Area of smaller circle
→ Area of shaded part = 616 - 154
→ Area of shaded part = 462
Therefore, the area of shaded part = 462 cm²
