An airforce plane is ascending vertically at the rate of 100 km/h. If the radius of the earth is `rk m ,` how fast is the area of the earth, visible from the plane, increasing at 3 minutes after it started ascending? Given that the visible area `A` at height `h` is given by `A=2pir^2h/(r+h)` .

Explanation

To solve the problem step by step, we will follow the given information and derive the required rate of change of the visible area from the plane.

**Step 1: Understand the given information**
- The plane ascends vertically at a rate of \( \frac{dh}{dt} = 100 \) km/h.
- The radius of the Earth is \( r \) km.
- The formula for the visible area \( A \) at height \( h \) is given by:
\[
A = \frac{2 \pi r^2 h}{r + h}
...