The problem states that if the circumference of a circle increases by 40%, what happens to the area of the circle? We need to find the percentage increase in the area.

1. Problem Description

The problem states that if the circumference of a circle increases by 40%, what happens to the area of the circle? We need to find the percentage increase in the area.

2. Solution Steps

Let $C$ be the original circumference and $A$ be the original area.

Let $C'$ be the new circumference and $A'$ be the new area.

The formulas for the circumference and area of a circle are:

$C = 2\pi r$

$A = \pi r^2$

Given that the circumference increases by 40%, we have:

$C' = C + 0.4C = 1.4C$

$2\pi r' = 1.4(2\pi r)$

$r' = 1.4r$

Now, let's find the new area $A'$:

$A' = \pi (r')^2 = \pi (1.4r)^2 = \pi (1.96r^2) = 1.96 \pi r^2 = 1.96A$

The increase in area is $A' - A = 1.96A - A = 0.96A$

The percentage increase in area is $\frac{A' - A}{A} \times 100\% = \frac{0.96A}{A} \times 100\% = 0.96 \times 100\% = 96\%$

3. Final Answer

The area increases by 96%.

Final Answer: E) aumenta 96%