# Redesign it!!Pay 'n' spray!!

Calculus Level 5

The GSRO(Gautam space research institute hypothetical) launches a large sprayer satellite into the atmoshere which orbits the earth in earth's equatorial orbit to paint it in a different colour. The range of sprayer is angle $$a$$ above the horizontal and below it as shown in figure.

Find half of area on earth surface which will never get sprayed.

Details

• Earth is stationary and at same horizontal level.
• Sprayer orbits earth in a circular path at a constant distance from earth's centre as shown.
• AB is tangent to earth.
• Take $$\cos a$$=$$\dfrac{4}{11}$$