# Crazy Calculus 6

Calculus Level pending

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

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