# Sphere + right triangle - problems

1. Spherical cap
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.
2. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
3. Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
4. Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
5. Sphere and cone
Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
6. Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
7. Felix
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
8. Horizon
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.]
9. Sphere - parts
Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
10. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
11. Moon
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.
12. Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
13. Spherical cap
What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
14. Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
15. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
16. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
17. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
18. Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
19. Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
20. Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?

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