Question

F the radius of a circle is increased by 20% then the area is increased by :

Answer 1

Answer:

Area is being increased by 44% of the old area.

Step-by-step explanation:

Let a circle with radius 'r',

= >  Area of the circle = πr^2    

         

According to the question, radius of the circle is increased by 20%

= >  New radius = Original radius + 20% of original radius

= >  New radius = r + ( 20 / 100 x r )

= >  New radius = r( 1 + 20 / 100 )

= >  New radius = r( 1 + 1 / 5 )

= >  New radius = r x ( 5 + 1 ) / 5

= >  New radius = r x 6 / 5

= >  New radius = 6r / 5

∴ Area of the circle with new radius = π ( 6r / 5 )^2

           ⇒ π x 6r / 5 x 6r / 5

           ⇒ 36πr^2 / 25

Then,

Increase in area = 36 / 25 πr^2 - 1 πr^2

                           = 11 / 25 πr^2

Increasing % = 11 / 25 πr^2 x 100

Increasing % = 44% πr^2

Increasing % = 44% of old area