Question

if the diameter of the circle increase by 40 % how much area of circle increased ? ​

Answer 1

40% increased in the circle also

Answer 2

Answer:

Area of circle will increase by 96%

Step-by-step explanation

Let "d" be the diameter of the original circle

Let "r" be the radius of the original circle

d = 2r

r = (d/2)

Since "r" and "d" are linearly related, a 40% increase in the diameter will automatically mean a 40% increase in the radius.

Let R be the radius of the new circle

=> R = 40% more than the radius of old circle

=> R is 40% more than r

=> R = r + 40% of r

=> R = r + 0.4*r

=> R = 1.4*r ......(i)

Let "a" be the area of the old circle

=> a = πr²

Let "A" be the area of the new circle

=> A = πR²

From (i), we get

A = π(1.4*r)²

A = π * 1.4² * r²

A = 1.96* (πr²)

A = 1.96*a

=> A = a + 0.96*a

=> A = a + (96/100)*a

=> A = a + 96% of a

=> Area of new circle is 96% more than area of old circle

=> Area of circle will increase by 96%