Q13. Calculate the area of a circular ring, whose internal and external radii are
3 cm and 10 cm respectively.
Answers
Step-by-step explanation:
Given :-
Internal and External radii of two circles are 3 cm and 10 cm
To find :-
Calculate the area of a circular ring ?
Solution :-
General Method :-
Given that
External radius of the circle = 10 cm
We know that
Area of a circle = πr² sq.units
=> Area = (22/7)×10² cm²
=> Area = (22/7)×100
=> Area = (22×100)/7
Area of the external circle = 2200/7 cm²
Internal radius of the circle = 3 cm
Area of the inner circle = (22/7)×3² cm²
=> Area = (22/7)×9
=> Area = (22×9)/7
=> Area = 198/7 cm²
Area of the circular ring
=> Area of the external circle - Area of the internal circle
=> (2200/7)-(198/7)
=> (2200-198)/7
=> 2002/7
=> 286 cm²
Formula method :-
If the external and internal radii of the circles are R and r units then Area of the circular ring is π(R²-r²) or π(R+r)(R-r) sq.units
We have ,
R = 10 cm
r = 3 cm
Area of the circular ring
=> (22/7)(10+3)(10-3)
=> (22/7)(13)(7)
=> 22×13
=> 286 cm²
Answer:-
Area of the circular ring for the given problem is 286 cm²
Used formulae :-
- If the external and internal radii of the circles are R and r units then Area of the circular ring is π(R²-r²) or π(R+r)(R-r) sq.units
- Area of a circle is πr² sq.units
Where, r = radius
- π = 22/7