If the circumference of a circle is increased by 11\(\frac{1}{9}\)%, then find the percentage increase in its area? - 

 23.45% increase

Let radius be r- 

Radius     Circumference    Area 

  r              2 \(\pi\)r         \(\pi\)r²

                     ↓   (changed values percentage change)

   ↓               \(\frac{10}{9}\)  2 \(\pi\)r  

 \(\frac{10}{9}\)r (the change in circumference is directly proportional to radius change)

Area =  \(\pi\)( \(\frac{10}{9}\)r)² = \(\pi\)( \(\frac{100}{81}\)r²) = 23.45% increase