Question

If the radius of a circle is increased by 40%.What will be its increase in area?

Answer 1

Area (A1) of circle with radius r is
= πr^2

When radius increase by 40%, that means new radius become,
= [r + 40% × r]
= [ r + (40/100)× r ]
= [ r +(2/5)×r]
= (7/5)×r
= 7r/5

Now Area of circle with radius 7r/5 is,
A2= π (7r/5)^2
= π[(49/25)r^2]

​​​​​​Increase in Area of circle is A2 - A1
= [ π(49/25)r^2 ] - [πr^2]
= (24/25) πr^2
= (24/25) *A1
= 0.96 × A1

So the Area of the circle is increased by 96 %