
Calculate the area of a circular ring whose outer and inner radii are and .
A.
B.
C.
D.
Answer
419.1k+ views
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 :
Where is the radius of the circle and is the mathematical constant, values .
Complete step by step answer:
Given, outer and inner radii are and respectively.
Let us consider the radius of the outer circle as and the radius of the inner circle as .
Radius of outer circle ,
Radius of inner circle,
We can find the area of the ring by subtracting the area of the outer circle and area of the inner circle.
⇒
First we can find the area of the outer circle with radius .
By substituting the values,
We get,
By multiplying,
We get,
Now we can find the area of the inner circle with radius .
By substituting the values,
We get,
By multiplying,
We get,
Now we can find the area of the ring,
By subtracting,
We get,
Thus we get the area of the circular ring is
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.
By taking common ,
We get ,
By substituting the values,
We get,
By simplifying,
We get,
By subtracting,
We get,
By multiplying,
We get,
Thus we get the area of the circular ring as
We can also find the area of the circular ring in this method.
Formula used :
Where
Complete step by step answer:

Given, outer and inner radii are
Let us consider the radius of the outer circle as
Radius of outer circle ,
Radius of inner circle,
We can find the area of the ring by subtracting the area of the outer circle and area of the inner circle.
⇒
First we can find the area of the outer circle with radius
By substituting the values,
We get,
By multiplying,
We get,
Now we can find the area of the inner circle with radius
By substituting the values,
We get,
By multiplying,
We get,
Now we can find the area of the ring,
By subtracting,
We get,
Thus we get the area of the circular ring is
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.
By taking
We get ,
By substituting the values,
We get,
By simplifying,
We get,
By subtracting,
We get,
By multiplying,
We get,
Thus we get the area of the circular ring as
We can also find the area of the circular ring in this method.
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