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Calculate the area of a circular ring whose outer and inner radii are 12 and 10 cm.
A.118.16 cm2
B.128.16 cm2
C.138.16 cm2
D.148.16 cm2

Answer
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Hint: In this question, we need to find the area of a circular ring. A ring is nothing but a space between two concentric circles. Concentric circles are circles with the same centre and different radius. We can find the area of the ring by subtracting the area of the outer circle and area of the inner circle.
Formula used :
Area of the circle =πr2
Where r is the radius of the circle and π is the mathematical constant, values 3.14 .

Complete step by step answer:
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Given, outer and inner radii are 12 cm and 10 cm respectively.
Let us consider the radius of the outer circle as R and the radius of the inner circle as r.
Radius of outer circle ,
R=12 cm
Radius of inner circle,
r=10 cm
We can find the area of the ring by subtracting the area of the outer circle and area of the inner circle.
Area of the ring = Area of the outer circle Area of the inner circle
First we can find the area of the outer circle with radius R=12 cm .
Area of the outer circle=πR2
By substituting the values,
We get,
Area=3.14×(12)2
By multiplying,
We get,
Area of the outer circle=452.16 cm2
Now we can find the area of the inner circle with radius r=10 cm.
Area of the inner circle=πr2
By substituting the values,
We get,
Area=3.14×(10)2
By multiplying,
We get,
Area of the inner circle=314 cm2
Now we can find the area of the ring,
Area of the ring = Area of the outer circle Area of the inner circle
Area of the ring=452.16314
By subtracting,
We get,
Area of the circular ring=138.16 cm2
Thus we get the area of the circular ring is 138.16 cm2

So, the correct answer is “Option C”.

Note:
Alternative solution :
We can find the area of the ring by subtracting the area of the outer circle and area of the inner circle.
Area of the ring = Area of the outer circle Area of the inner circle
Area=πR2πr2
By taking π common ,
We get ,
Area=π(R2r2)
By substituting the values,
We get,
Area=3.14((12)2(10)2)
By simplifying,
We get,
Area=3.14(144100)
By subtracting,
We get,
Area=3.14×(44)
By multiplying,
We get,
Area=138.16
Thus we get the area of the circular ring as 138.16 cm2
We can also find the area of the circular ring in this method.