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.


  • 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.
  • Earth's radius R=6371 kilometres.
  • Take \(\cos a\)=\(\dfrac{4}{11}\)
  • Give answer in metre square unit.

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