Crazy Calculus 6

An air force plane is ascending vertically at the rate of $100\text{ km/hr}$ . If the radius of the Earth is $R \text{ km}$ , how fast is the area of the Earth visible from the plane increasing at 3 minutes after it started ascending?

Take visible area $A=\dfrac { 2\pi R^ 2H }{ R+H }$ , where $H$ is the height of the plane (in $\text{km}$ ) above the Earth.

P : $\frac { 200\pi r^ 3 }{ (R+5)^ 2 }$ $\frac { km^ 2 }{ h }$

Q : $\frac { 200\pi r^ 3 }{ (R+5) }$ $\frac { km^ 2 }{ h }$

R : $\frac { 400\pi r^ 3 }{ (R+5) }$ $\frac { km^ 2 }{ h }$

S : $\frac { 400\pi r^ 3 }{ (R+5)^ 2 }$ $\frac { km^ 2 }{ h }$