PART-A
:- Find the area of a circle whose circumference is 62.5 cm.
Answers
Answer :
Area of the circle = 310.53 cm²
Given :
• Circumference of circle = 62.5 cm
To find :
• Area of the circle
Concept :
Firstly, we will calculate the radius of the circle by substituting the values in the formula of circumference of circle. From there we will get the value of radius. After getting the value of radius of circle substitute it in the formula of area of circle. The resultant value will be the required answer.
Formula of circumference of circle :-
- Circumference of circle = 2πr
Formula of area of circle :-
- Area of circle = πr²
where,
• Take π = 22/7
• r denotes the radius of the circle
The unit of circumference (Perimeter) is m, cm, etc.
The unit of area is m², cm², etc.
Solution :
Radius of the circle :-
⠀⠀⠀⇒ Circumference = 2πr
⠀⠀⠀⇒ Substituting the given values :
⠀⠀⠀⇒ 62.5 = 2 × 22/7 × r
⠀⠀⠀⇒ 62.5 = 44/7 × r
⠀⠀⠀⇒ Transposing 44/7 to the left hand side, ⠀⠀⠀on transposing the denominator will become ⠀⠀⠀numerator and the numerator will become ⠀⠀⠀denominator.
⠀⠀⠀⇒ 62.5 × 7/44 = r
⠀⠀⠀⇒ 437.5/44 = r
⠀⠀⠀⇒ 9.94 = r
Radius of the circle = 9.94 cm
Area of circle :-
⠀⠀⠀⇒ Area of circle = πr²
⠀⠀⠀⇒ Substituting the given values :
⠀⠀⠀⇒ Area of circle = 22/7 × (9.94)²
⠀⠀⠀⇒ Area of circle = 22/7 × 9.94 × 9.94
⠀⠀⠀⇒ Area of circle = 310.53
Area of the circle = 310.53 cm²
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Verification :
We can verify the value of radius by calculating the value of circumference, if it will equal to 62.5 cm (as mentioned in the question) then the value of radius is right.
⠀⠀⠀⇒ Circumference = 2πr
⠀⠀⠀⇒ Circumference = 2 × 22/7 × 9.94
⠀⠀⠀⇒ Circumference = 62.48
62.48 can be rounded off to 62.5
Therefore, circumference of the circle = 62.5 cm
Hence, verified.