If the circumference of a circle is increased by 11\(\frac{1}{9}\)%, then find the percentage increase in its area? -
Answer & explanation
Correct answer: option 2
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