Sphere + triangle - problems

  1. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  2. Rotation of the Earth
    earth_1 Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
  3. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  4. Horizon
    lighthouse The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  5. Moon
    zem_mesic We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
  6. Airplane
    tu-144 Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
  7. Sphere from tree points
    sphere2_1 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  8. Pilot
    aircraft-02_12 How high is the airplane's pilot to see 0.001 of Earth's surface?
  9. Spherical cap
    gulovy_odsek Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
  10. Earth's circumference
    parallels Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.

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