If the circumference of a circle is doubled what happens to the area
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ANSWER :
- Before increasing circumference :
Circumference of circle = 2πr
Circumference = 2 * 22/7 * r
=> r = Circumference ÷ 44/7
=> r = Circumference * 7 / 44
Area of circle = πr^2
Area of circle = 22/7*( C x 7/44 )^2
=> Area of circle = 7C^2/88..... (1)
- Doubling the circumference :
2 * Circumference = 2πr
=> 2 * C = 44/7 * r
=> r = 7C/22
Area of circle = πr^2
=> Area = 22/7*( 7C/22 )^2
=> Area = 7C^2/22.......(2)
Subtracting (1) from (2) :
=> 7C^2/22 - 7C^2/88 = 21C^2/88
21C^2/88 = 3(7C^2/88)
But 7C^2/88 is original area
=> Area increase = 3*Original Area
Therefore, area of circle increases by 3 times when circumference is doubled.
Hope this helps you☺☺
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