Question

If the circumference of a circle is doubled what happens to the area

Answer 1

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☺☺